# Characteristic cycles and Gevrey series solutions of $A$-hypergeometric systems

## TL;DR

This paper computes characteristic cycles of $A$-hypergeometric systems and their homology modules, analyzes the multiplicities' semicontinuity, and studies the Gevrey solution spaces' behavior, advancing understanding of these complex systems.

## Contribution

It introduces new methods for calculating characteristic cycles and multiplicities, and applies these to analyze Gevrey solutions of $A$-hypergeometric systems.

## Key findings

- Computed $L$-characteristic cycles and Euler-Koszul homology modules.
- Proved upper semicontinuity of multiplicities in characteristic cycles.
- Analyzed the behavior of Gevrey solution spaces.

## Abstract

We compute the $L$-characteristic cycle of an $A$-hypergeometric system and higher Euler-Koszul homology modules of the toric ring. We also prove upper semicontinuity results about the multiplicities in these cycles and apply our results to analyze the behavior of Gevrey solution spaces of the system.