Publication Date

2001

Journal or Book Title

COMPOSITIO MATHEMATICA

Abstract

Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors projectively dual to torus orbit closures. We show that most of these potential denominators never appear in rational hypergeometric functions. We conjecture that the denominator of any rational hypergeometric function is a product of resultants, that is, a product of special discriminants arising from Cayley configurations. This conjecture is proved for toric hypersurfaces and for toric varieties of dimension at most three. Toric residues are applied to show that every toric resultant appears in the denominator of some rational hypergeometric function.

Comments

This is the pre-published version harvested from ArXiv. The published version is located at http://www.springerlink.com/content/w4v50p487725632n/

Pages

217-239

Volume

128

Issue

2

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