Isomorphism Classes of A-Hypergeometric Systems
Mutsumi Saito · Compositio Mathematica · 2001
Given a finite set A of integral vectors and a parameter vector, Gel'fand, Kapranov, and Zelevinskii defined a system of differential equations, 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.