Isomorphism classes of A-hypergeometric systems

1999/12/28 by Mutsumi Saito, Saito, Mutsumi · 2 citations
Computer Science · Engineering · Mathematics · #16S32 (Secondary) #33C70 (Primary) 14M25 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14M25 #msc:16S32 #msc:33C70

paper · pdf · doi:10.48550/arxiv.math/9912213

16 pages, LaTeX

arxiv created 1999/12/28 · openalex publication_date 1999/12/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite set A of integral vectors, Gel'fand, Kapranov and Zelevinskii defined a system of differential equations with a parameter vector as a D-module, which system is called an A-hypergeometric (or a GKZ hypergeometric) system. Classifying the parameters according to the D-isomorphism classes of their corresponding A-hypergeometric systems is one of the most fundamental problems in the theory. In this paper we give a combinatorial answer for the problem under the assumption that the finite set A lies in a hyperplane off the origin, and illustrate it in two particularly simple cases: the normal case and the monomial curve case.

Cited by

• Comprehensive Restriction Algorithm for Hypergeometric Systems
• Gevrey expansions of hypergeometric integrals I

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