关于一般型曲面上除数的内洁性的一个注解

Pub Date : 2022-11-10 DOI:10.1556/012.2022.01532

Debojyoti Bhattacharya, Joyentanuj Das

{"title":"关于一般型曲面上除数的内洁性的一个注解","authors":"Debojyoti Bhattacharya, Joyentanuj Das","doi":"10.1556/012.2022.01532","DOIUrl":null,"url":null,"abstract":"Let X be an irreducible complex projective variety of dimension n ≥ 1. Let D be a Cartier divisor on X such that Hi(X, OX (mD)) = 0 for m > 0 and for all i > 0, then it is not true in general that D is a nef divisor (cf. [4]). Also, in general, effective divisors on smooth surfaces are not necessarily nef (they are nef provided they are semiample). In this article, we show that, if X is a smooth surface of general type and C is a smooth hyperplane section of it, then for any non-zero effective divisor D on X satisfying H1(X, OX (mD)) = 0 for all m > C.KX, D is a nef divisor.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Remark on Nefness of Divisors on Surfaces of General Type\",\"authors\":\"Debojyoti Bhattacharya, Joyentanuj Das\",\"doi\":\"10.1556/012.2022.01532\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let X be an irreducible complex projective variety of dimension n ≥ 1. Let D be a Cartier divisor on X such that Hi(X, OX (mD)) = 0 for m > 0 and for all i > 0, then it is not true in general that D is a nef divisor (cf. [4]). Also, in general, effective divisors on smooth surfaces are not necessarily nef (they are nef provided they are semiample). In this article, we show that, if X is a smooth surface of general type and C is a smooth hyperplane section of it, then for any non-zero effective divisor D on X satisfying H1(X, OX (mD)) = 0 for all m > C.KX, D is a nef divisor.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1556/012.2022.01532\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1556/012.2022.01532","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X为维数n≥1的不可约复射影变数。设D是X上的一个Cartier除数，使得Hi(X, OX (mD))在m > 0且对于所有i > 0时均为0，则D一般不成立为nef除数(参见[4])。此外，一般来说，光滑表面上的有效除数不一定是净的(只要它们是半样本的，它们是净的)。在本文中，我们证明了，如果X是一般类型的光滑曲面，C是它的光滑超平面截面，那么对于X上的任意非零有效因子D满足H1(X, OX (mD)) = 0，对于所有m > C. kx, D是一个净因子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

A Remark on Nefness of Divisors on Surfaces of General Type

Let X be an irreducible complex projective variety of dimension n ≥ 1. Let D be a Cartier divisor on X such that Hi(X, OX (mD)) = 0 for m > 0 and for all i > 0, then it is not true in general that D is a nef divisor (cf. [4]). Also, in general, effective divisors on smooth surfaces are not necessarily nef (they are nef provided they are semiample). In this article, we show that, if X is a smooth surface of general type and C is a smooth hyperplane section of it, then for any non-zero effective divisor D on X satisfying H1(X, OX (mD)) = 0 for all m > C.KX, D is a nef divisor.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助