Differential zeros of period integrals and generalized hypergeometric functions

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.

35 pages, minor corrections made

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