INVESTIGADORES
DICKENSTEIN Alicia Marcela
artículos
Título:
The A-hypergeometric System Associated with a Monomial Curve
Autor/es:
E. CATTANI, C. D'ANDREA Y A. DICKENSTEIN
Revista:
DUKE MATHEMATICAL JOURNAL
Editorial:
DUKE UNIV PRESS
Referencias:
Año: 1999 vol. 99 p. 179 - 207
ISSN:
0012-7094
Resumen:
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.