Exceptional Parameters for Generic A-Hypergeometric Systems

A-hypergeometric systems are systems of linear partial differential equations with polynomial coefficients that can be built out of a toric ideal and a parameter vector. Homogeneous toric ideals are themselves built out of combinatorial data, n distinct integer points lying in a hyperplane off the origin in d-dimensional space. We may assume that these points are the columns of a d×n integer matrix whose first row is made up of ones. Definition 1.1. A d × n matrix A whose columns are distinct elements of {1} × Z and generate Z as a lattice is said to be homogeneous. Set m = n− d.