{"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}
引用次数: 0
Abstract
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.
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.
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