Vol. 6, No. 3, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Resonance equals reducibility for $A$-hypergeometric systems

Mathias Schulze and Uli Walther

Vol. 6 (2012), No. 3, 527–537
Abstract

Classical theorems of Gel’fand et al. and recent results of Beukers show that nonconfluent Cohen–Macaulay A-hypergeometric systems have reducible monodromy representation if and only if the continuous parameter is A-resonant.

We remove both the confluence and Cohen–Macaulayness conditions while simplifying the proof.

Keywords
toric, hypergeometric, Euler–Koszul, $D$-module, resonance, monodromy
Mathematical Subject Classification 2010
Primary: 13N10
Secondary: 32S40, 14M25
Milestones
Received: 1 October 2010
Revised: 4 January 2011
Accepted: 22 February 2011
Published: 5 July 2012
Authors
Mathias Schulze
Department of Mathematics
Oklahoma State University
Stillwater, OK 74078
United States
Uli Walther
Department of Mathematics
Purdue University
150 North University Street
West Lafayette, IN 47907-2067
United States