Rational Hypergeometric Functions

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dc.creatorCattani, Eduardo
dc.creatorDickenstein, Alicia
dc.creatorSturmfels, Bernd
dc.date1999-11-04
dc.date.accessioned2026-07-07T05:31:27Z
dc.date.available2026-07-07T05:31:27Z
dc.descriptionMultivariate 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.
dc.descriptionLaTeX, 26 pages
dc.identifierhttps://arxiv.org/abs/math/9911030
dc.identifierhttp://arxiv.org/abs/math/9911030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79347
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.titleRational Hypergeometric Functions
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