{"title":"库兹涅佐夫通过 Hochschild-Serre 代数的法诺三折猜想","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":"{\"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}","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}
Kuznetsov’s Fano threefold conjecture via Hochschild–Serre algebra
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
