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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Lehn, M"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.11686">arXiv:2206.11686</a> <span> [<a href="https://arxiv.org/pdf/2206.11686">pdf</a>, <a href="https://arxiv.org/format/2206.11686">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Czapli%C5%84ski%2C+A">Adam Czapli艅ski</a>, <a href="/search/math?searchtype=author&query=Krug%2C+A">Andreas Krug</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Rollenske%2C+S">S枚nke Rollenske</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.11686v2-abstract-short" style="display: inline;"> We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalises Kodaira's classification of singular elliptic fibres and thus call them extended ADE curves. On such a curve $C$, we describe a compactified Jacobian and show that its components reflect the intersection graph of $C$. This extends known results when $C$ is reduced, but n… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.11686v2-abstract-full').style.display = 'inline'; document.getElementById('2206.11686v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.11686v2-abstract-full" style="display: none;"> We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalises Kodaira's classification of singular elliptic fibres and thus call them extended ADE curves. On such a curve $C$, we describe a compactified Jacobian and show that its components reflect the intersection graph of $C$. This extends known results when $C$ is reduced, but new difficulties arise when $C$ is non-reduced. As an application, we get an explicit description of general singular fibres of certain Lagrangian fibrations of Beauville-Mukai type. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.11686v2-abstract-full').style.display = 'none'; document.getElementById('2206.11686v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Minor corrections. To appear in Commun. Contemp. Math</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1709.05951">arXiv:1709.05951</a> <span> [<a href="https://arxiv.org/pdf/1709.05951">pdf</a>, <a href="https://arxiv.org/ps/1709.05951">ps</a>, <a href="https://arxiv.org/format/1709.05951">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> On the stability of flat complex vector bundles over parallelizable manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Biswas%2C+I">Indranil Biswas</a>, <a href="/search/math?searchtype=author&query=Dumitrescu%2C+S">Sorin Dumitrescu</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1709.05951v2-abstract-short" style="display: inline;"> We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / 螕$, where $G$ is a complex connected Lie group and $螕$ is a cocompact lattice in it. The main result proved here is a structure theorem for flat holomorphic vector bundles $E_蟻$ associated to any irreducible representation $蟻: 螕\rightarrow \text{GL}(r,{\mathbb C})$. More precisely, we prove that… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1709.05951v2-abstract-full').style.display = 'inline'; document.getElementById('1709.05951v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1709.05951v2-abstract-full" style="display: none;"> We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / 螕$, where $G$ is a complex connected Lie group and $螕$ is a cocompact lattice in it. The main result proved here is a structure theorem for flat holomorphic vector bundles $E_蟻$ associated to any irreducible representation $蟻: 螕\rightarrow \text{GL}(r,{\mathbb C})$. More precisely, we prove that $E_蟻$ is holomorphically isomorphic to a vector bundle of the form $E^{\oplus n}$, where $E$ is a stable vector bundle. All the rational Chern classes of $E$ vanish, in particular, its degree is zero. We deduce a stability result for flat holomorphic vector bundles $E_蟻$ of rank 2 over $G/ 螕$. If an irreducible representation $蟻: 螕\rightarrow \text{GL}(2, \mathbb {C})$ satisfies the conditionmthat the induced homomorphism $螕\rightarrow {\rm PGL}(2, {\mathbb C})$ does not extend to a homomorphism from $G$, then $E_蟻$ is proved to be stable. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1709.05951v2-abstract-full').style.display = 'none'; document.getElementById('1709.05951v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 August, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 September, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Comptes Rendus Math茅matique (to appear)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 53B21; 53C56; 53A55 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1609.04573">arXiv:1609.04573</a> <span> [<a href="https://arxiv.org/pdf/1609.04573">pdf</a>, <a href="https://arxiv.org/ps/1609.04573">ps</a>, <a href="https://arxiv.org/format/1609.04573">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lahoz%2C+M">Mart铆 Lahoz</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Macr%C3%AC%2C+E">Emanuele Macr矛</a>, <a href="/search/math?searchtype=author&query=Stellari%2C+P">Paolo Stellari</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1609.04573v3-abstract-short" style="display: inline;"> We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic eightfold $Z$, described by the four authors, is isomorphic to an irreducible component of a moduli space of Gieseker stable torsion sheaves or rank three torsion fre… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1609.04573v3-abstract-full').style.display = 'inline'; document.getElementById('1609.04573v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1609.04573v3-abstract-full" style="display: none;"> We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic eightfold $Z$, described by the four authors, is isomorphic to an irreducible component of a moduli space of Gieseker stable torsion sheaves or rank three torsion free sheaves. For a very general such cubic fourfold, we show that $Z$ is isomorphic to a connected component of a moduli space of tilt-stable objects in the derived category and to a moduli space of Bridgeland stable objects in the Kuznetsov component. Moreover, the contraction between $Z'$ and $Z$ is realized as a wall-crossing in tilt-stability. Finally, $Z$ is birational to an irreducible component of Gieseker stable aCM bundles of rank six. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1609.04573v3-abstract-full').style.display = 'none'; document.getElementById('1609.04573v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 September, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">34 pages. Minor revisions. Final version to appear in J. Math. Pures Appl</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1604.04121">arXiv:1604.04121</a> <span> [<a href="https://arxiv.org/pdf/1604.04121">pdf</a>, <a href="https://arxiv.org/format/1604.04121">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Symplectic Geometry">math.SG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1112/S0010437X16008277">10.1112/S0010437X16008277 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Towards a symplectic version of the Chevalley restriction theorem </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bulois%2C+M">Michael Bulois</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+C">Christian Lehn</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Terpereau%2C+R">Ronan Terpereau</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1604.04121v2-abstract-short" style="display: inline;"> If $(G,V)$ is a polar representation with Cartan subspace $\mathfrak c$ and Weyl group $W$, it is shown that there is a natural morphism of Poisson schemes $\mathfrak c \oplus {\mathfrak c}^*/W \to V\oplus V^*/\!\!/\!\!/ G$. This morphism is conjectured to be an isomorphism of the underlying reduced varieties if $(G,V)$ is visible. The conjecture is proved for visible stable locally free polar rep… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1604.04121v2-abstract-full').style.display = 'inline'; document.getElementById('1604.04121v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1604.04121v2-abstract-full" style="display: none;"> If $(G,V)$ is a polar representation with Cartan subspace $\mathfrak c$ and Weyl group $W$, it is shown that there is a natural morphism of Poisson schemes $\mathfrak c \oplus {\mathfrak c}^*/W \to V\oplus V^*/\!\!/\!\!/ G$. This morphism is conjectured to be an isomorphism of the underlying reduced varieties if $(G,V)$ is visible. The conjecture is proved for visible stable locally free polar representations and certain further examples. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1604.04121v2-abstract-full').style.display = 'none'; document.getElementById('1604.04121v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 March, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 April, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, final version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 14L30; 53D20; 20G05; 20G20; 13A50 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Compositio Math. 153 (2017) 647-666 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1404.5657">arXiv:1404.5657</a> <span> [<a href="https://arxiv.org/pdf/1404.5657">pdf</a>, <a href="https://arxiv.org/ps/1404.5657">ps</a>, <a href="https://arxiv.org/format/1404.5657">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1515/crelle-2014-0145">10.1515/crelle-2014-0145 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On the symplectic eightfold associated to a Pfaffian cubic fourfold </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Addington%2C+N">N. Addington</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">M. Lehn</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1404.5657v2-abstract-short" style="display: inline;"> We show that the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface. We do this by constructing for a generic Pfaffian cubic Y a birational map Z ---> Hilb^4(X), where X is the K3 surface associated to Y by Beauville and Donagi. We interpret Z as a moduli space of comp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1404.5657v2-abstract-full').style.display = 'inline'; document.getElementById('1404.5657v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1404.5657v2-abstract-full" style="display: none;"> We show that the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface. We do this by constructing for a generic Pfaffian cubic Y a birational map Z ---> Hilb^4(X), where X is the K3 surface associated to Y by Beauville and Donagi. We interpret Z as a moduli space of complexes on X and observe that at some point of Z, hence on a Zariski open subset, the complex is just the ideal sheaf of four points. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1404.5657v2-abstract-full').style.display = 'none'; document.getElementById('1404.5657v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 June, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 April, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages. Minor changes; to appear in Crelle as an appendix to 1305.0178</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. reine angew. Math. 731:129-137, 2017 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1305.0178">arXiv:1305.0178</a> <span> [<a href="https://arxiv.org/pdf/1305.0178">pdf</a>, <a href="https://arxiv.org/format/1305.0178">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> Twisted cubics on cubic fourfolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lehn%2C+C">Christian Lehn</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Sorger%2C+C">Christoph Sorger</a>, <a href="/search/math?searchtype=author&query=van+Straten%2C+D">Duco van Straten</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1305.0178v2-abstract-short" style="display: inline;"> We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space M_3(Y) of twisted cubics on a smooth cubic fourfold Y that does not contain a plane is shown to be smooth and to admit a contraction M_3(Y) -> Z(Y) to a projective eight-dimensional symplectic manifold Z(Y). The construction is based on results on… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1305.0178v2-abstract-full').style.display = 'inline'; document.getElementById('1305.0178v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1305.0178v2-abstract-full" style="display: none;"> We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space M_3(Y) of twisted cubics on a smooth cubic fourfold Y that does not contain a plane is shown to be smooth and to admit a contraction M_3(Y) -> Z(Y) to a projective eight-dimensional symplectic manifold Z(Y). The construction is based on results on linear determinantal representations of singular cubic surfaces. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1305.0178v2-abstract-full').style.display = 'none'; document.getElementById('1305.0178v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 July, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 May, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">A proof that Z(Y) is simply-connected and irreducible hyperk盲hler has been added. A couple of typos corrected</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 14C05; 14C21; 14J10; Secondary 14J26; 14J35; 14J70 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1002.4107">arXiv:1002.4107</a> <span> [<a href="https://arxiv.org/pdf/1002.4107">pdf</a>, <a href="https://arxiv.org/ps/1002.4107">ps</a>, <a href="https://arxiv.org/format/1002.4107">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1112/S0010437X11005550">10.1112/S0010437X11005550 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Slodowy Slices and Universal Poisson Deformations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lehn%2C+M">M. Lehn</a>, <a href="/search/math?searchtype=author&query=Namikawa%2C+Y">Y. Namikawa</a>, <a href="/search/math?searchtype=author&query=Sorger%2C+C">Ch. Sorger</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1002.4107v3-abstract-short" style="display: inline;"> We classify the nilpotent orbits in a simple Lie algebra for which the restriction of the adjoint quotient map to a Slodowy slice is the universal Poisson deformation of its central fibre. This generalises work of Brieskorn and Slodowy on subregular orbits. In particular, we find in this way new singular symplectic hypersurfaces of dimension 4 and 6. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1002.4107v3-abstract-full" style="display: none;"> We classify the nilpotent orbits in a simple Lie algebra for which the restriction of the adjoint quotient map to a Slodowy slice is the universal Poisson deformation of its central fibre. This generalises work of Brieskorn and Slodowy on subregular orbits. In particular, we find in this way new singular symplectic hypersurfaces of dimension 4 and 6. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1002.4107v3-abstract-full').style.display = 'none'; document.getElementById('1002.4107v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 March, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 February, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">29 p. Minor changes. Final version. To appear in Compositio Mathematica</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 14B07; 17B45; 17B63 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Compositio Math. 148 (2012) 121-144 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0810.3225">arXiv:0810.3225</a> <span> [<a href="https://arxiv.org/pdf/0810.3225">pdf</a>, <a href="https://arxiv.org/ps/0810.3225">ps</a>, <a href="https://arxiv.org/format/0810.3225">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> A symplectic resolution for the binary tetrahedral group </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Sorger%2C+C">Christoph Sorger</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0810.3225v2-abstract-short" style="display: inline;"> We describe an explicit symplectic resolution for the quotient singularity arising from the four-dimensional symplectic represenation of the binary tetrahedral group. </span> <span class="abstract-full has-text-grey-dark mathjax" id="0810.3225v2-abstract-full" style="display: none;"> We describe an explicit symplectic resolution for the quotient singularity arising from the four-dimensional symplectic represenation of the binary tetrahedral group. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0810.3225v2-abstract-full').style.display = 'none'; document.getElementById('0810.3225v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 May, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 October, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0504202">arXiv:math/0504202</a> <span> [<a href="https://arxiv.org/pdf/math/0504202">pdf</a>, <a href="https://arxiv.org/ps/math/0504202">ps</a>, <a href="https://arxiv.org/format/math/0504202">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s00222-005-0484-6">10.1007/s00222-005-0484-6 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Singular symplectic moduli spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Kaledin%2C+D">Dmitry Kaledin</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Sorger%2C+C">Christoph Sorger</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0504202v1-abstract-short" style="display: inline;"> Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O'Grady. Consequently, since singular moduli space that do not belong to these exceptional cases have singularities in codimension $\geq4$ they do no ad… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0504202v1-abstract-full').style.display = 'inline'; document.getElementById('math/0504202v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0504202v1-abstract-full" style="display: none;"> Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O'Grady. Consequently, since singular moduli space that do not belong to these exceptional cases have singularities in codimension $\geq4$ they do no admit projective symplectic resolutions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0504202v1-abstract-full').style.display = 'none'; document.getElementById('math/0504202v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 April, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 14J60; Secondary 14D20; 14J28; 32J27 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0504182">arXiv:math/0504182</a> <span> [<a href="https://arxiv.org/pdf/math/0504182">pdf</a>, <a href="https://arxiv.org/ps/math/0504182">ps</a>, <a href="https://arxiv.org/format/math/0504182">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> La singularit茅 de O'Grady </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Sorger%2C+C">Christoph Sorger</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0504182v2-abstract-short" style="display: inline;"> Let M be the moduli space of semistable sheaves with Mukai vector 2v on an abelian or K3 surface where v is primitive such that <v,v>=2. We show that the blow-up of the reduced singular locus of M provides a symplectic resolution of singularities. This gives a direct description of O'Grady's resolutions of M\_{K3}(2,0,4) and M\_{Ab}(2,0,2). </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0504182v2-abstract-full" style="display: none;"> Let M be the moduli space of semistable sheaves with Mukai vector 2v on an abelian or K3 surface where v is primitive such that <v,v>=2. We show that the blow-up of the reduced singular locus of M provides a symplectic resolution of singularities. This gives a direct description of O'Grady's resolutions of M\_{K3}(2,0,4) and M\_{Ab}(2,0,2). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0504182v2-abstract-full').style.display = 'none'; document.getElementById('math/0504182v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 March, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 April, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">In French. Major revision. Final version. To appear in Journal of Algebraic Geometry</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 14J60; Secondary 14D20; 14J28 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0405575">arXiv:math/0405575</a> <span> [<a href="https://arxiv.org/pdf/math/0405575">pdf</a>, <a href="https://arxiv.org/ps/math/0405575">ps</a>, <a href="https://arxiv.org/format/math/0405575">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> Local structure of hyperkaehler singularities in O'Grady's examples </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Kaledin%2C+D">D. Kaledin</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">M. Lehn</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0405575v2-abstract-short" style="display: inline;"> We study the local structure of the singularity in the moduli space of sheaves on a K3 surface which has been resolved by K O'Grady in his construction of new examples of hyperkaehler manifolds. In particular, we identify the singularity with the closure of a certain nilpotent orbit in the coadjoint representation of the group $Sp(4)$. We also prove that the moduli spaces for some other sets of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0405575v2-abstract-full').style.display = 'inline'; document.getElementById('math/0405575v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0405575v2-abstract-full" style="display: none;"> We study the local structure of the singularity in the moduli space of sheaves on a K3 surface which has been resolved by K O'Grady in his construction of new examples of hyperkaehler manifolds. In particular, we identify the singularity with the closure of a certain nilpotent orbit in the coadjoint representation of the group $Sp(4)$. We also prove that the moduli spaces for some other sets of numerical parameters do not admit a smooth symplectic resolution of singularities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0405575v2-abstract-full').style.display = 'none'; document.getElementById('math/0405575v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 March, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 May, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, LaTeX2e. Final version, to appear in MMJ</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0012166">arXiv:math/0012166</a> <span> [<a href="https://arxiv.org/pdf/math/0012166">pdf</a>, <a href="https://arxiv.org/ps/math/0012166">ps</a>, <a href="https://arxiv.org/format/math/0012166">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> The cup product of the Hilbert scheme for K3 surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Sorger%2C+C">Christoph Sorger</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0012166v1-abstract-short" style="display: inline;"> To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A^[n] in such a way that for any smooth projective surface X with trivial canonical divisor there is a canonical isomorphism of rings between (H*X)^[n] and the cohomology H*(X^[n]) of the n-th Hilbert scheme of X. </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0012166v1-abstract-full" style="display: none;"> To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A^[n] in such a way that for any smooth projective surface X with trivial canonical divisor there is a canonical isomorphism of rings between (H*X)^[n] and the cohomology H*(X^[n]) of the n-th Hilbert scheme of X. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0012166v1-abstract-full').style.display = 'none'; document.getElementById('math/0012166v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 December, 2000; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2000. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 14C05; 14C1520B30;17B68; 17B69; 20C05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0009131">arXiv:math/0009131</a> <span> [<a href="https://arxiv.org/pdf/math/0009131">pdf</a>, <a href="https://arxiv.org/ps/math/0009131">ps</a>, <a href="https://arxiv.org/format/math/0009131">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> Symmetric groups and the cup product on the cohomology of Hilbert schemes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a>, <a href="/search/math?searchtype=author&query=Sorger%2C+C">Christoph Sorger</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0009131v2-abstract-short" style="display: inline;"> The integral cohomology ring of the Hilbert scheme of n-tuples on the affine plane is shown to be isomorphic to the graded ring associated to a filtration of the ring of integral class functions on the symmetric group. </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0009131v2-abstract-full" style="display: none;"> The integral cohomology ring of the Hilbert scheme of n-tuples on the affine plane is shown to be isomorphic to the graded ring associated to a filtration of the ring of integral class functions on the symmetric group. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0009131v2-abstract-full').style.display = 'none'; document.getElementById('math/0009131v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 December, 2000; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 September, 2000; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2000. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages. Minor corrections, reference added. To appear in: Duke Math. Journal</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 14C05; 14C15; 20B30; 17B68; 17B69; 20C05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/9904095">arXiv:math/9904095</a> <span> [<a href="https://arxiv.org/pdf/math/9904095">pdf</a>, <a href="https://arxiv.org/ps/math/9904095">ps</a>, <a href="https://arxiv.org/format/math/9904095">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> On the Cobordism Class of the Hilbert Scheme of a Surface </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ellingsrud%2C+G">G. Ellingsrud</a>, <a href="/search/math?searchtype=author&query=G%C3%B6ttsche%2C+L">L. G枚ttsche</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">M. Lehn</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/9904095v1-abstract-short" style="display: inline;"> Let S be a smooth projective surfaces and S^[n] the Hilbert scheme of zero-dimensional subschemes of S of length n. We proof that the class of S^[n] in the complex cobordism ring depends only on the class of the surface itself. Moreover, we compute the cohomology and holomorphic Euler characterisitcs of certain tautological sheaves on S^[n] and prove results on the general structure of certain i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9904095v1-abstract-full').style.display = 'inline'; document.getElementById('math/9904095v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/9904095v1-abstract-full" style="display: none;"> Let S be a smooth projective surfaces and S^[n] the Hilbert scheme of zero-dimensional subschemes of S of length n. We proof that the class of S^[n] in the complex cobordism ring depends only on the class of the surface itself. Moreover, we compute the cohomology and holomorphic Euler characterisitcs of certain tautological sheaves on S^[n] and prove results on the general structure of certain integrals over polynomials in Chern classes of tautological sheaves. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9904095v1-abstract-full').style.display = 'none'; document.getElementById('math/9904095v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 April, 1999; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 1999. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, Latex 2e</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 14C05;14Q10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/9803091">arXiv:math/9803091</a> <span> [<a href="https://arxiv.org/pdf/math/9803091">pdf</a>, <a href="https://arxiv.org/ps/math/9803091">ps</a>, <a href="https://arxiv.org/format/math/9803091">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s002220050307">10.1007/s002220050307 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Chern Classes of Tautological Sheaves on Hilbert Schemes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/9803091v1-abstract-short" style="display: inline;"> We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification of the cohomology ring of Hilbert schemes of the affine plane with a ring of differential operators on a Fock space. We end with the computation of the top Se… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9803091v1-abstract-full').style.display = 'inline'; document.getElementById('math/9803091v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/9803091v1-abstract-full" style="display: none;"> We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification of the cohomology ring of Hilbert schemes of the affine plane with a ring of differential operators on a Fock space. We end with the computation of the top Segre classes of tautological bundles associated to line bundles on Hilb^n up to n=7, and give a conjecture for the generating series. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9803091v1-abstract-full').style.display = 'none'; document.getElementById('math/9803091v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 March, 1998; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 1998. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">45 pages, LaTeX</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 14C05 (primary); 14C17; 14Q10 (secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/alg-geom/9704016">arXiv:alg-geom/9704016</a> <span> [<a href="https://arxiv.org/pdf/alg-geom/9704016">pdf</a>, <a href="https://arxiv.org/ps/alg-geom/9704016">ps</a>, <a href="https://arxiv.org/format/alg-geom/9704016">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> On the irreducibility of the punctual Quotient Scheme of a Surface </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ellingsrud%2C+G">Geir Ellingsrud</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="alg-geom/9704016v1-abstract-short" style="display: inline;"> We prove that the Quot-scheme of finite quotients of a vector bundle which are of a given length and supported in one point, is irreducible and of the expected dimension. </span> <span class="abstract-full has-text-grey-dark mathjax" id="alg-geom/9704016v1-abstract-full" style="display: none;"> We prove that the Quot-scheme of finite quotients of a vector bundle which are of a given length and supported in one point, is irreducible and of the expected dimension. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('alg-geom/9704016v1-abstract-full').style.display = 'none'; document.getElementById('alg-geom/9704016v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 April, 1997; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 1997. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, Latex2e</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/alg-geom/9211001">arXiv:alg-geom/9211001</a> <span> [<a href="https://arxiv.org/pdf/alg-geom/9211001">pdf</a>, <a href="https://arxiv.org/ps/alg-geom/9211001">ps</a>, <a href="https://arxiv.org/format/alg-geom/9211001">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> Stable pairs on curves and surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Huybrechts%2C+D">Daniel Huybrechts</a>, <a href="/search/math?searchtype=author&query=Lehn%2C+M">Manfred Lehn</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="alg-geom/9211001v2-abstract-short" style="display: inline;"> We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider two examples. The fixed sheaf is the structure sheaf or is a vector bundle on a divisor, i.e. Higgs pairs or framed bundles, resp. (unencoded version) </span> <span class="abstract-full has-text-grey-dark mathjax" id="alg-geom/9211001v2-abstract-full" style="display: none;"> We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider two examples. The fixed sheaf is the structure sheaf or is a vector bundle on a divisor, i.e. Higgs pairs or framed bundles, resp. (unencoded version) <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('alg-geom/9211001v2-abstract-full').style.display = 'none'; document.getElementById('alg-geom/9211001v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 November, 1992; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 November, 1992; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 1992. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">37 pages, LaTeX Version 2.09, MPI-92-093</span> </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> 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