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# Communications in Number Theory and Physics

## Volume 12 (2018)

### Number 4

### Differential zeros of period integrals and generalized hypergeometric functions

Pages: 609 – 655

DOI: https://dx.doi.org/10.4310/CNTP.2018.v12.n4.a1

#### Authors

#### Abstract

In this paper, we study the zero loci of locally constant sheaves 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 $V^{\mathsf{v}} = \Gamma (X, K^{-1}{X})$. 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.

Received 17 January 2018

Accepted 14 June 2018

Published 14 January 2019