{"title":"On the problem of rationality for some cubic complexes","authors":"A. Alzati , M. Bertolini","doi":"10.1016/S1385-7258(88)80015-5","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>V</em> be the complete intersection of smooth, generic quadric and cubic hypersurfaces in ℙ<sup>5</sup>(ℂ). <em>V</em> is a non rational Fano threefold. It is interesting to study the rationality of <em>V</em> when it contains <em>n</em> planes. This problem has been solved when the planes meet two by two in one point only. We consider and solve all remaining cases.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 349-364"},"PeriodicalIF":0.0000,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80015-5","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725888800155","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Let V be the complete intersection of smooth, generic quadric and cubic hypersurfaces in ℙ5(ℂ). V is a non rational Fano threefold. It is interesting to study the rationality of V when it contains n planes. This problem has been solved when the planes meet two by two in one point only. We consider and solve all remaining cases.
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