{"title":"Kuznetsov’s Fano threefold conjecture via Hochschild–Serre algebra","authors":"Xun Lin, Shizhuo Zhang","doi":"10.1007/s00209-024-03586-6","DOIUrl":null,"url":null,"abstract":"<p>Let <i>Y</i> be a smooth quartic double solid regarded as a degree 4 hypersurface of the weighted projective space <span>\\(\\mathbb {P}(1,1,1,1,2)\\)</span>. We study the multiplication of the Hochschild-Serre algebra of its Kuznetsov component <span>\\(\\mathcal {K}u(Y)\\)</span> via matrix factorization. As an application, we give a new disproof of Kuznetsov’s Fano threefold conjecture.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Zeitschrift","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00209-024-03586-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Let Y be a smooth quartic double solid regarded as a degree 4 hypersurface of the weighted projective space \(\mathbb {P}(1,1,1,1,2)\). We study the multiplication of the Hochschild-Serre algebra of its Kuznetsov component \(\mathcal {K}u(Y)\) via matrix factorization. As an application, we give a new disproof of Kuznetsov’s Fano threefold conjecture.
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