Characteristic cycles and Gevrey series solutions of A-hypergeometric systems

Berkesch, Christine; Fernández-Fernández, María-Cruz

doi:10.2140/ant.2020.14.323

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

Christine Berkesch and María-Cruz Fernández-Fernández

Vol. 14 (2020), No. 2, 323–347

DOI: 10.2140/ant.2020.14.323

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.

Keywords

$A$-hypergeometric system, toric ring, $D$-module, characteristic cycle, irregularity sheaf, Gevrey series

Mathematical Subject Classification 2010

Primary: 13N10

Secondary: 14M25, 32C38, 33C70

Milestones

Received: 12 February 2019

Revised: 25 September 2019

Accepted: 13 November 2019

Published: 17 March 2020

Authors

Christine Berkesch
School of Mathematics University of Minnesota Minneapolis, MN United States

María-Cruz Fernández-Fernández
Departamento de Álgebra e Instituto de Matemáticas-IMUS Universidad de Sevilla Spain

Vol. 14, No. 2, 2020