Cattani, E. (Eduardo), 1946-D'Andrea, Carlos, 1973-Dickenstein, Alicia2009-08-192009-08-1919990012-7094https://hdl.handle.net/2445/9170We 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 + 1.29 p.application/pdfeng(c) Duke University Press, 1999Funcions hipergeomètriquesGeometria algebraicaOther hypergeometric functions and integrals in several variablesFamilies, fibrationsDeformations of analytic structuresBasic hypergeometric functions of one variableinfo:eu-repo/semantics/article544297info:eu-repo/semantics/openAccess