Differential forms on universal K3 surfaces

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2024-07-12 DOI:10.1017/s0305004124000100

SHOUHEI MA

{"title":"Differential forms on universal K3 surfaces","authors":"SHOUHEI MA","doi":"10.1017/s0305004124000100","DOIUrl":null,"url":null,"abstract":"We give a vanishing and classification result for holomorphic differential forms on smooth projective models of the moduli spaces of pointed K3 surfaces. We prove that there is no nonzero holomorphic k-form for $0<k<10$ and for even $k>19$ . In the remaining cases, we give an isomorphism between the space of holomorphic k-forms with that of vector-valued modular forms ( $10\\leq k \\leq 18$ ) or scalar-valued cusp forms (odd $k\\geq 19$ ) for the modular group. These results are in fact proved in the generality of lattice-polarisation.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"7 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Cambridge Philosophical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0305004124000100","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

We give a vanishing and classification result for holomorphic differential forms on smooth projective models of the moduli spaces of pointed K3 surfaces. We prove that there is no nonzero holomorphic k-form for

$0<k<10$

and for even

$k>19$

. In the remaining cases, we give an isomorphism between the space of holomorphic k-forms with that of vector-valued modular forms (

$10\leq k \leq 18$

) or scalar-valued cusp forms (odd

$k\geq 19$

) for the modular group. These results are in fact proved in the generality of lattice-polarisation.

查看原文本刊更多论文

通用 K3 表面上的微分形式

我们给出了尖 K3 曲面模空间光滑投影模型上的全形微分形式的消失和分类结果。我们证明，在 $0<k<10$ 和偶数 $k>19$ 时，不存在非零的全形 k 形式。在其余情况下，我们给出了全形 k 形式空间与模数群的矢量值模数形式（$10\leq k \leq 18$）或标量值尖顶形式（奇$k\geq 19$）空间之间的同构关系。这些结果实际上是在格极化的一般性中证明的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.