2000/12/28 by Mutsumi Saito, Saito, Mutsumi · 1 citation
Computer Science · Mathematics · #13N10 #14M25 #16S32 #33C70 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13N10 #msc:14M25 #msc:16S32 #msc:33C70
paper · pdf · doi:10.48550/arxiv.math/0012257
20 pages, 2 figures, LaTeX2e
arxiv created 2000/12/28 · openalex publication_date 2000/12/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a dimension formula for the space of logarithm-free series solutions to an A-hypergeometric (or a GKZ hypergeometric) system. In the case where the convex hull spanned by A is a simplex, we give a rank formula for the system, characterize the exceptional set, and prove the equivalence of the Cohen-Macaulayness of the toric variety defined by A with the emptiness of the exceptional set. Furthermore we classify A-hypergeometric systems as analytic D-modules.