{"title":"表面","authors":"Eleanor Chan","doi":"10.4324/9780429326431-5","DOIUrl":null,"url":null,"abstract":". Let S be a smooth projective algebraic surface satisfying the following property: H i ( S,B ) = 0 for i > 0, for any irreducible and reduced curve B of S . The aim of this paper is to provide a characterization of special linear systems on S which are singular along a set of double points in very general position. As an application, the dimension of such systems is evaluated in case S is a simple Abelian surface, a K 3 surface which does not contain elliptic curves or an anticanonical rational surface.","PeriodicalId":272977,"journal":{"name":"Mathematics and the Craft of Thought in the Anglo-Dutch Renaissance","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Surface\",\"authors\":\"Eleanor Chan\",\"doi\":\"10.4324/9780429326431-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let S be a smooth projective algebraic surface satisfying the following property: H i ( S,B ) = 0 for i > 0, for any irreducible and reduced curve B of S . The aim of this paper is to provide a characterization of special linear systems on S which are singular along a set of double points in very general position. As an application, the dimension of such systems is evaluated in case S is a simple Abelian surface, a K 3 surface which does not contain elliptic curves or an anticanonical rational surface.\",\"PeriodicalId\":272977,\"journal\":{\"name\":\"Mathematics and the Craft of Thought in the Anglo-Dutch Renaissance\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics and the Craft of Thought in the Anglo-Dutch Renaissance\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4324/9780429326431-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and the Craft of Thought in the Anglo-Dutch Renaissance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4324/9780429326431-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
． 设S为光滑射影代数曲面，满足以下性质:对于任意S的不可约约曲线B，当i > 0时，H i (S,B) = 0。本文的目的是给出S上沿非常一般位置上的一组双点奇异的特殊线性系统的一个刻划。作为应用，在S为简单阿贝尔曲面、不含椭圆曲线的k3曲面或反正则有理曲面的情况下，计算了这类系统的维数。
. Let S be a smooth projective algebraic surface satisfying the following property: H i ( S,B ) = 0 for i > 0, for any irreducible and reduced curve B of S . The aim of this paper is to provide a characterization of special linear systems on S which are singular along a set of double points in very general position. As an application, the dimension of such systems is evaluated in case S is a simple Abelian surface, a K 3 surface which does not contain elliptic curves or an anticanonical rational surface.
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