广义Kummer型hyperkähler流形的一般基点自由性

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-11-16 DOI:10.1007/s12188-023-00271-z

Mauro Varesco

{"title":"广义Kummer型hyperkähler流形的一般基点自由性","authors":"Mauro Varesco","doi":"10.1007/s12188-023-00271-z","DOIUrl":null,"url":null,"abstract":"<div><p>We study base-point-freeness for big and nef line bundles on hyperkähler manifolds of generalized Kummer type: For <span>\\(n\\in \\{2,3,4\\}\\)</span>, we show that, generically in all but a finite number of irreducible components of the moduli space of polarized <span>\\(\\textrm{Kum}^n\\)</span>-type varieties, the polarization is base-point-free. We also prove generic base-point-freeness in the moduli space in all dimensions if the polarization has divisibility one.\n</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Towards generic base-point-freeness for hyperkähler manifolds of generalized Kummer type\",\"authors\":\"Mauro Varesco\",\"doi\":\"10.1007/s12188-023-00271-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study base-point-freeness for big and nef line bundles on hyperkähler manifolds of generalized Kummer type: For <span>\\\\(n\\\\in \\\\{2,3,4\\\\}\\\\)</span>, we show that, generically in all but a finite number of irreducible components of the moduli space of polarized <span>\\\\(\\\\textrm{Kum}^n\\\\)</span>-type varieties, the polarization is base-point-free. We also prove generic base-point-freeness in the moduli space in all dimensions if the polarization has divisibility one.\\n</p></div>\",\"PeriodicalId\":50932,\"journal\":{\"name\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-11-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s12188-023-00271-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s12188-023-00271-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了广义Kummer型hyperkähler流形上的大束和网束的基点自由性:对于\(n\in \{2,3,4\}\)，我们证明了除了有限数量的偏振\(\textrm{Kum}^n\)型变体的模空间的不可约分量外，一般的偏振是无基点的。如果极化可整除为1，则证明了模空间在所有维度上的一般基点自由性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Towards generic base-point-freeness for hyperkähler manifolds of generalized Kummer type

We study base-point-freeness for big and nef line bundles on hyperkähler manifolds of generalized Kummer type: For \(n\in \{2,3,4\}\), we show that, generically in all but a finite number of irreducible components of the moduli space of polarized \(\textrm{Kum}^n\)-type varieties, the polarization is base-point-free. We also prove generic base-point-freeness in the moduli space in all dimensions if the polarization has divisibility one.

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

来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.