Hypergeometric Functions for Projective Toric Curves

TL;DR

This paper analyzes the parameter space of A-hypergeometric systems related to projective monomial curves, providing a detailed decomposition that clarifies the solutions' analytic behavior.

Contribution

It introduces a novel decomposition of the parameter space into lines and their complement, enabling explicit analysis of solution behaviors.

Findings

Parameter space decomposed into lines and complement

Explicit control over solution behavior within each region

Enhanced understanding of hypergeometric system solutions

Abstract

We produce a decomposition of the parameter space of the $A$-hypergeometric system associated to a projective monomial curve as a union of an arrangement of lines and its complement, in such a way that the analytic behavior of the solutions of the system is explicitly controlled within each term of the union.