Logarithm-free A-hypergeometric series

Details Logarithm-free A-hypergeometric series Logarithm-free A-hypergeometric series

2000-12-28

arxiv.org/abs/math/0012257v1

Mathematics

Algebraic Geometry

20 pages, 2 figures, LaTeX2e

Scientific paper

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.

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