{"title":"Bott vanishing for Fano threefolds","authors":"Burt Totaro","doi":"10.1007/s00209-024-03468-x","DOIUrl":null,"url":null,"abstract":"<p>Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that <span>\\(H^j(X,\\Omega ^i_X\\otimes L)=0\\)</span> for <span>\\(j>0\\)</span>, <span>\\(i\\ge 0\\)</span>, and <i>L</i> ample. This holds for toric varieties, but not for most other varieties. We classify the smooth Fano threefolds that satisfy Bott vanishing. There are many more than expected.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"208 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-04-20","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/s00209-024-03468-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that \(H^j(X,\Omega ^i_X\otimes L)=0\) for \(j>0\), \(i\ge 0\), and L ample. This holds for toric varieties, but not for most other varieties. We classify the smooth Fano threefolds that satisfy Bott vanishing. There are many more than expected.
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