{"title":"On some finite ramified coverings of Pn","authors":"Tsuyoshi Fujiwara","doi":"10.1016/S1385-7258(87)80002-1","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>S</em> be a hypersurface in <em>P</em><sup><em>n</em></sup> (<em>n</em>≧3) with only normal crossings and let ƒ : <em>X</em><strong>P</strong><sup><em>n</em></sup> be a finite ramified covering which is unramified over <strong>P</strong><sup><em>n</em></sup> − <em>S</em>. Then S. Kawai has shown that there are neither regular 1-forms nor regular 2-forms on <em>X</em>. The aim of this article is to derive a stronger conclusion: <em>H</em><sup>0</sup>(<em>X,Ω</em><sub><em>X</em></sub><sup><em>p</em></sup>)= 0 for 1≦p<<em>n</em> , and moreover <em>H</em><sup>0</sup>(<em>X,Ω</em><sub><em>X</em></sub><sup><em>p</em></sup>)= 0 if deg <em>S</em>≦<em>n</em>+1.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"90 1","pages":"Pages 7-13"},"PeriodicalIF":0.0000,"publicationDate":"1987-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(87)80002-1","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725887800021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Let S be a hypersurface in Pn (n≧3) with only normal crossings and let ƒ : XPn be a finite ramified covering which is unramified over Pn − S. Then S. Kawai has shown that there are neither regular 1-forms nor regular 2-forms on X. The aim of this article is to derive a stronger conclusion: H0(X,ΩXp)= 0 for 1≦p<n , and moreover H0(X,ΩXp)= 0 if deg S≦n+1.
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