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Irreducible quotients of A-hypergeometric systems

Part of: Special varieties Rings and algebras arising under various constructions

Published online by Cambridge University Press:  17 August 2010

Mutsumi Saito
Mutsumi Saito*
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan (email: saito@math.sci.hokudai.ac.jp)
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Abstract

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Gel’fand, Kapranov and Zelevinsky proved, using the theory of perverse sheaves, that in the Cohen–Macaulay case an A-hypergeometric system is irreducible if its parameter vector is non-resonant. In this paper we prove, using the theory of the ring of differential operators on an affine toric variety, that in general an A-hypergeometric system is irreducible if and only if its parameter vector is non-resonant. In the course of the proof, we determine the irreducible quotients of an A-hypergeometric system.

Keywords

A-hypergeometric systemsirreducibilityresonancetoric varietyring of differential operators

MSC classification

Secondary: 33C70: Other hypergeometric functions and integrals in several variables 16S32: Rings of differential operators 14M25: Toric varieties, Newton polyhedra
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 2 , March 2011 , pp. 613 - 632
Copyright
Copyright © Foundation Compositio Mathematica 2010

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