Characteristic cycles and gevrey series solutions of a-hypergeometric systems

Christine Berkesch, María Cruz Fernández-Fernández

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)323-347
Number of pages25
JournalAlgebra and Number Theory
Volume14
Issue number2
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
CB was partially supported by NSF Grants DMS 1661962, DMS 1440537, OISE 0964985. MCFF was partially supported by MTM2016-75024-P, PP2014-2397, P12-FQM-2696 and FEDER. MSC2010: primary 13N10; secondary 14M25, 32C38, 33C70. Keywords: A-hypergeometric system, toric ring, D-module, characteristic cycle, irregularity sheaf, Gevrey series.

Funding Information:
CB was partially supported by NSF Grants DMS 1661962, DMS 1440537, OISE 0964985. MCFF was partially supported by MTM2016-75024-P, PP2014-2397, P12-FQM-2696 and FEDER.We are grateful to Francisco Jes?s Castro Jim?nez, Laura Felicia Matusevich, and Uli Walther for helpful conversations related to this work. Fern?ndez-Fern?ndez would like to thank the School of Mathematics of the University of Minnesota for the hospitality during her visit to work on this paper with Berkesch.

Publisher Copyright:
© 2020, Mathematical Sciences Publishers. All rights reserved.

Keywords

  • A-hypergeometric system
  • Characteristic cycle
  • D-module
  • Gevrey series
  • Irregularity sheaf
  • Toric ring

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