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Title: The A-hypergeometric system associated with a monomial curve
Author: Cattani, E. (Eduardo), 1946-
D'Andrea, Carlos, 1973-
Dickenstein, Alicia
Keywords: Funcions hipergeomètriques
Geometria algebraica
Other hypergeometric functions and integrals in several variables
Families, fibrations
Deformations of analytic structures
Basic hypergeometric functions of one variable
Issue Date: 1999
Publisher: Duke University Press
Abstract: We make a detailed analysis of the A-hypergeometric system (or GKZ system) associated with a monomial curve and integral, hence resonant, exponents. We characterize the Laurent polynomial solutions and show that these are the only rational solutions. We also show that for any exponent, there are at most two linearly independent Laurent solutions, and that the upper bound is reached if and only if the curve is not arithmetically Cohen--Macaulay. We then construct, for all integral parameters, a basis of local solutions in terms of the roots of the generic univariate polynomial associated with A. We determine the holonomic rank r for all integral exponents and show that it is constantly equal to the degree d of X if and only if X is arithmetically Cohen-Macaulay. Otherwise there is at least one exponent for which r = d + 1.
Note: Reproducció del document publicat a
It is part of: Duke Mathematical Journal, 1999, vol. 99, núm. 2, p. 179-207.
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ISSN: 0012-7094
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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