{"title":"On the non-rationality of the Fano variety of ℙ5, which contains three planes two by two meeting in one point","authors":"Elisabetta Ambrogio , Daniela Romagnoli","doi":"10.1016/S1385-7258(89)80012-5","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that the Fano variety <em>W</em> of degree 6 in ℙ<sup>5</sup>, complete intersection of a smooth quadric hypersurface with a smooth cubic hypersurface of ℙ<sup>5</sup>, is not rational if it contains 3 planes two by two meeting at least in one point.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 1","pages":"Pages 15-19"},"PeriodicalIF":0.0000,"publicationDate":"1989-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80012-5","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725889800125","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that the Fano variety W of degree 6 in ℙ5, complete intersection of a smooth quadric hypersurface with a smooth cubic hypersurface of ℙ5, is not rational if it contains 3 planes two by two meeting at least in one point.
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