Document Zbl 07991482

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Math.</a> <a href="/?q=in%3A524678" title="Articles in this Issue">80, No. 2, Paper No. 51, 22 p. (2025)</a>. </div> <div class="abstract">Summary: We define the minimal plus-one generated curves and prove a result explaining why they are the closest relatives of the free curves, after the nearly free curves. Then we look at the projective closures of the general and of the special fibers of some Briançon-type polynomials constructed by E. Artal Bartolo, Pi. Cassou-Noguès and I. Luengo Velasco. They yield new examples of free, nearly free or minimal plus-one generated curves, as well as counter-examples to the conjecture saying that a supersolvable curve is free. In the final section we give a characterization of plus-one generated curves in terms of eigenscheme ideals, similar to the characterization of free curves given by R. Di Gennaro, G. Ilardi, R.M. Miró-Roig, H. Schenck and J. Vallès in a recent paper. Then we apply this result to the construction of minimal plus-one generated curves obtained by putting together at least two members in a pencil of curves related to Briançon-type polynomials.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A14H50" title="MSC2020">14H50</a> </td> <td class="space"> Plane and space curves </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A13D02" title="MSC2020">13D02</a> </td> <td class="space"> Syzygies, resolutions, complexes and commutative rings </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aplane+curve">plane curve</a>; <a href="/?q=ut%3AMilnor+algebra">Milnor algebra</a>; <a href="/?q=ut%3Aminimal+resolution">minimal resolution</a>; <a href="/?q=ut%3AMilnor+and+Tjurina+number">Milnor and Tjurina number</a>; <a href="/?q=ut%3ABrian%C3%A7on-type+polynomial">Briançon-type polynomial</a></div> <div class="software"> <h3>Software:</h3><a href="/software/866">SINGULAR</a></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 07991482" data-ciurl="/ci/07991482" data-biburl="/bibtex/07991482.bib" data-amsurl="/amsrefs/07991482.bib" data-xmlurl="/xml/07991482.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07991482.pdf" title="Zbl 07991482 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/10.1007/s00025-025-02371-z" aria-label="DOI for “Plus-one generated curves, Briançon-type polynomials and eigenscheme ideals”" title="10.1007/s00025-025-02371-z">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2406.19795"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abe, T., Plus-one generated and next to free arrangements of hyperplanes, Int. 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