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Article

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Published version

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1999

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/9170

The A-hypergeometric system associated with a monomial curve

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http://dx.doi.org/10.1215/S0012-7094-99-09908-8

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.

Subject

Funcions hipergeomètriques, Geometria algebraica

Subject (English)

Other hypergeometric functions and integrals in several variables, Families, fibrations, Deformations of analytic structures, Basic hypergeometric functions of one variable

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CATTANI, E. (Eduardo), D'ANDREA, Carlos and DICKENSTEIN, Alicia. The A-hypergeometric system associated with a monomial curve. Duke Mathematical Journal. 1999. Vol. 99, num. 2, pags. 179-207. ISSN 0012-7094. [consulted: 9 of August of 2026]. Available at: https://hdl.handle.net/2445/9170

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