GENERALISED AUTOMORPHIC SHEAVES AND THE PROPORTIONALITY PRINCIPLE OF HIRZEBRUCH-MUMFORD

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-10 DOI:10.1017/s1474748023000300

Fritz Hörmann

引用次数: 0

Abstract

Abstract We axiomatise the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalised automorphic sheaf is proposed which includes sheaves of (meromorphic) sections of automorphic vector bundles with prescribed vanishing and pole orders along strata in the compactification, and their quotients. These include, for instance, sheaves of Jacobi forms and weakly holomorphic modular forms. Using this machinery, we give a short and purely algebraic proof of the proportionality theorem of Hirzebruch and Mumford.

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广义自同构轴与hirzebruch-mumford的比例原理

摘要给出了(混合)Shimura变及其自同构向量束环面紧化的代数性质的公理化。提出了广义自同构束的概念，该概念包括紧化中沿地层具有规定消失和极点阶的自同构向量束的(亚纯)截面束及其商。例如，它们包括雅可比形式和弱全纯模形式。利用这一机制，我们给出了Hirzebruch和Mumford的比例定理的一个简短的纯代数证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.