Vol. 14, No. 2, 2020

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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
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