Document Zbl 1524.14041

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Sigma</a> <a href="/?q=in%3A476475" title="Articles in this Issue">10, Paper No. e63, 33 p. (2022)</a>. </div> <div class="abstract">Summary: In this paper, we prove a stronger form of the Bogomolov-Gieseker (BG) inequality for stable sheaves on two classes of Calabi-Yau threefolds, namely, weighted hypersurfaces inside the weighted projective spaces $\mathbb{P}(1, 1, 1, 1, 2)$ and $\mathbb{P}(1, 1, 1, 1, 4)$. Using the stronger BG inequality as a main technical tool, we construct open subsets in the spaces of Bridgeland stability conditions on these Calabi-Yau threefolds.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7577488">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A14F08" title="MSC2020">14F08</a> </td> <td class="space"> Derived categories of sheaves, dg categories, and related constructions in algebraic geometry </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A14J60" title="MSC2020">14J60</a> </td> <td class="space"> Vector bundles on surfaces and higher-dimensional varieties, and their moduli </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A14J33" title="MSC2020">14J33</a> </td> <td class="space"> Mirror symmetry (algebro-geometric aspects) </td> </tr></table> </div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1524.14041" data-ciurl="/ci/07577488" data-biburl="/bibtex/07577488.bib" data-amsurl="/amsrefs/07577488.bib" data-xmlurl="/xml/07577488.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07577488.pdf" title="Zbl 1524.14041 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1017/fms.2022.58" aria-label="DOI for “Stability conditions on Calabi-Yau double/triple solids”" title="10.1017/fms.2022.58">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2007.00044"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Arcara, D. and Bertram, A., ‘Bridgeland-stable moduli spaces for $K$ -trivial surfaces’, J. 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Soc.120(575) (1996), viii+ 88. · <a href="/0849.16011" class="nowrap">Zbl 0849.16011</a></td> </tr><tr> <td>[9]</td> <td class="space">Kanazawa, A. and Wilson, P. M. H., ‘Trilinear forms and Chern classes of Calabi-Yau threefolds’, Osaka J. Math.51(1) (2014), 203-213. · <a href="/1299.14035" class="nowrap">Zbl 1299.14035</a></td> </tr><tr> <td>[10]</td> <td class="space">Koseki, N., ‘Stability conditions on product threefolds of projective spaces and abelian varieties’, Bull. Lond. Math. Soc.50(2) (2017), 229-244. · <a href="/1428.14029" class="nowrap">Zbl 1428.14029</a></td> </tr><tr> <td>[11]</td> <td class="space">Koseki, N., ‘Stability conditions on threefolds with nef tangent bundles’, Adv. Math.372 (2020), 107316, 29. · <a href="/1440.14091" class="nowrap">Zbl 1440.14091</a></td> </tr><tr> <td>[12]</td> <td class="space">Li, C., ‘On stability conditions for the quintic threefold’, Invent. Math.218(1) (2019), 301-340. · <a href="/1431.14010" class="nowrap">Zbl 1431.14010</a></td> </tr><tr> <td>[13]</td> <td class="space">Li, C., ‘Stability conditions on Fano threefolds of Picard number 1’, J. Eur. Math. Soc. (JEMS)21(3) (2019), 709-726. · <a href="/1409.14034" class="nowrap">Zbl 1409.14034</a></td> </tr><tr> <td>[14]</td> <td class="space">Liu, S., ‘Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces’, Preprint, 2021, arXiv:2108.08934.</td> </tr><tr> <td>[15]</td> <td class="space">Liu, Y., ‘Stability conditions on product varieties’, J. Reine Angew. Math.770 (2021), 135-157. · <a href="/1468.14040" class="nowrap">Zbl 1468.14040</a></td> </tr><tr> <td>[16]</td> <td class="space">Maciocia, A., ‘Computing the walls associated to Bridgeland stability conditions on projective surfaces’, Asian J. Math.18(2) (2014), 263-279. · <a href="/1307.14022" class="nowrap">Zbl 1307.14022</a></td> </tr><tr> <td>[17]</td> <td class="space">Maciocia, A. and Piyaratne, D., ‘Fourier-Mukai transforms and Bridgeland stability conditions on abelian threefolds’, Algebr. Geom.2(3) (2015), 270-297. · <a href="/1322.14040" class="nowrap">Zbl 1322.14040</a></td> </tr><tr> <td>[18]</td> <td class="space">Maciocia, A. and Piyaratne, D., ‘Fourier-Mukai transforms and Bridgeland stability conditions on abelian threefolds II’, Internat. J. Math.27(1) (2016), 1650007. · <a href="/1360.14064" class="nowrap">Zbl 1360.14064</a></td> </tr><tr> <td>[19]</td> <td class="space">Macrì, E., ‘A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space’, Algebra Number Theory8(1):173-190, 2014. · <a href="/1308.14016" class="nowrap">Zbl 1308.14016</a></td> </tr><tr> <td>[20]</td> <td class="space">Martinez, C. and Schmidt, B., ‘Bridgeland stability on blow ups and counterexamples’, Math. 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IMRN (8) (2017), 2562-2566. · <a href="/1405.14097" class="nowrap">Zbl 1405.14097</a></td> </tr><tr> <td>[25]</td> <td class="space">Toda, Y., ‘Gepner type stability conditions on graded matrix factorizations’, Algebr. Geom.1(5) (2014), 613-665. · <a href="/1322.14042" class="nowrap">Zbl 1322.14042</a></td> </tr><tr> <td>[26]</td> <td class="space">Toda, Y., ‘Gepner point and strong Bogomolov-Gieseker inequality for quintic 3-folds’, in Higher Dimensional Algebraic Geometry—In Honour of Professor Yujiro Kawamata’s Sixtieth Birthday, Adv. Stud. Pure Math., vol. 74 (Math. Soc. Japan, Tokyo, 2017), 381-405. · <a href="/1388.14064" class="nowrap">Zbl 1388.14064</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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