Differential zeros of period integrals and generalized hypergeometric functions

Jingyue Chen; An Huang; Bong H. Lian; Shing-Tung Yau

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arXiv · 1709.00713

Differential zeros of period integrals and generalized hypergeometric functions

Jingyue Chen·An Huang·Bong H. Lian·Shing-Tung Yau

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Abstract

In this paper, we study the zero loci of local systems of the form $δΠ$, where $Π$ is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space $X$, and $δ$ is a given differential operator on the space of sections $V^\vee=Γ(X,K_X^{-1})$. Using earlier results of three of the authors and their collaborators, we give several different descriptions of the zero locus of $δΠ$. 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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BibTeX RIS

Jingyue Chen, An Huang, Bong H. Lian, Shing-Tung Yau. 2018-11-04. Differential zeros of period integrals and generalized hypergeometric functions. https://arxiv.org/abs/1709.00713

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