Differential zeros of period integrals and generalized hypergeometric functions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-09-03 DOI:10.4310/CNTP.2018.V12.N4.A1

Jingyue Chen, An Huang, B. Lian, S. Yau

引用次数: 1

Abstract

In this paper, we study the zero loci of local systems of the form $\delta\Pi$, where $\Pi$ is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space $X$, and $\delta$ is a given differential operator on the space of sections $V^\vee=\Gamma(X,K_X^{-1})$. Using earlier results of three of the authors and their collaborators, we give several different descriptions of the zero locus of $\delta\Pi$. As applications, we prove that the locus is algebraic and in some cases, non-empty. We also give an explicit way to compute the polynomial defining equations of the locus in some cases. This description gives rise to a natural stratification to the zero locus.

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周期积分的微分零与广义超几何函数

本文研究了形式为$\delta\Pi$的局部系统的零轨迹，其中$\Pi$是适当的环境空间$X$中CY超曲面泛族的周期轴，$\delta$是截面空间$V^\vee=\Gamma(X,K_X^{-1})$上的一个给定微分算子。利用三位作者及其合作者的早期结果，我们对$\delta\Pi$的零轨迹给出了几种不同的描述。作为应用，我们证明了轨迹是代数的，并且在某些情况下是非空的。在某些情况下，我们还给出了一种计算轨迹多项式定义方程的显式方法。这种描述导致了零轨迹的自然分层。

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.