Maximal Degeneracy Points of GKZ Systems

TL;DR

This paper investigates special boundary points called maximal degeneracy points in GKZ hypergeometric systems, revealing their significance in mirror symmetry and Calabi-Yau period integrals.

Contribution

It introduces the concept of maximal degeneracy points in GKZ systems and proves their existence at certain boundary points in the parameter space.

Findings

Existence of maximal degeneracy points at boundary points

All but one solutions become singular at these points

Relevance to mirror symmetry and Calabi-Yau manifolds

Abstract

Motivated by mirror symmetry, we study certain integral representations of solutions to the Gel'fand-Kapranov-Zelevinsky(GKZ) hypergeometric system. Some of these solutions arise as period integrals for Calabi-Yau manifolds in mirror symmetry. We prove that for a suitable compactification of the parameter space, there exists certain special boundary points, which we called maximal degeneracy points, at which all but one solutions become singular.