Este artículo es de Acceso Abierto y puede ser descargado en su versión final desde nuestro repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor


We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions. We also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank. © 2004 Elsevier Inc. All rights reserved.


Documento: Artículo
Título:Bivariate hypergeometric D-modules
Autor:Dickenstein, A.; Matusevich, L.F.; Sadykov, T.
Filiación:Dto. de Matemática, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Department of Mathematics, Harvard University, Cambridge, MA 02138, United States
Department of Mathematics, The University of Western Ontario, London, Ont. N6A 5B7, Canada
Palabras clave:Holonomic D-module; Holonomic rank; Horn system; Hypergeometric function
Página de inicio:78
Página de fin:123
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.


  • Adolphson, A., Hypergeometric functions and rings generated by monomials (1994) Duke Math. J., 73 (2), pp. 269-290
  • Björk, J.-E., (1979) Rings of Differential Operators, , Amsterdam: North-Holland Publishing Company
  • Cattani, E., (2003), personal communication; Cox, D., Little, J., O'Shea, D., An introduction to computational algebraic geometry and commutative algebra (1997) Ideals, Varieties and Algorithms, Undergraduate Texts in Mathematics, , Springer, New York, second ed
  • Dickenstein, A., Sturmfels, B., Elimination theory in codimension 2 (2002) J. Symbolic Comput., 34 (2), pp. 119-135
  • Eisenbud, D., With a view toward algebraic geometry (1995) Commutative Algebra, , New York: Springer
  • Eisenbud, D., Sturmfels, B., Binomial ideals (1996) Duke Math. J., 84 (1), pp. 1-45
  • Erdélyi, A., Hypergeometric functions of two variables (1950) Acta Math., 83, pp. 131-164
  • Euler, L., (1748) Introductio in Analysis Infinitorum, 1. , Laussane
  • Fischer, K.G., Shapiro, J., Mixed matrices and binomial ideals (1996) J. Pure Appl. Algebra, 113, pp. 39-54
  • Gauss, C.F., Disquisitiones generales circa seriem infinitam (1866), Thesis, Göttingen, 1812; in Ges. Werke, Göttingen; Gel'fand, I.M., Graev, M.I., Retakh, V.S., General hypergeometric systems of equations and series of hypergeometric type (1992) Uspekhi Mat. Nauk, 47, pp. 3-82. , 4(286)
  • Gel'fand, I.M., Graev, M.I., Zelevinsky, A.V., Holonomic systems of equations and series of hypergeometric type (1987) Dokl. Akad. Nauk SSSR, 295 (1), pp. 14-19
  • Gel'fand, I.M., Kapranov, M.M., Zelevinsky, A.V., Hypergeometric functions and toric varieties (1989) Funktsional. Anal. I Prilozhen., 23 (2), pp. 12-26
  • Grayson, D.R., Stillman, M.E., Macaulay 2, a software system for research in algebraic geometry, available at; Hoşten, S., Shapiro, J., Primary decomposition of lattice basis ideals (2000) J. Symbolic Comput., 29 (4-5), pp. 625-639
  • Hotta, R., Equivariant D-modules (1991) Proceedings of ICPAM Spring School in Wuhan, , P. Torasso (Ed.) Travaux en Cours, Paris
  • Kalkbrener, M., Sturmfels, B., Initial complexes of prime ideals (1995) Adv. Math., 116 (2), pp. 365-376
  • Kummer, E.E., Über die hypergeometrische Reihe F(α, β, γ, x) (1836) J. Math., 15
  • Matusevich, L.F., Exceptional parameters for generic A-hypergeometric systems (2003) Int. Math. Res. Not., 2003 (22), pp. 1225-1248
  • Passare, M., Sadykov, T.M., Tsikh, A.K., Singularities of nonconfluent hypergeometric functions in several variables Comp. Math., ,, to appear, available online at
  • Riemann, G.F.B., P-Funktionen (1857) Ges. Math. Werke, pp. 67-84. , Göttingen (Republished Leipzig 1892)
  • Sadykov, T.M., On the Horn system of partial differential equations and series of hypergeometric type (2002) Math. Scand., 91 (1), pp. 127-149
  • Saito, M., Logarithm-free A-hypergeometric series (2002) Duke Math. J., 115 (1), pp. 53-73
  • Saito, M., Sturmfels, B., Takayama, N., (2000) Gröbner Deformations of Hypergeometric Differential Equations, , Berlin: Springer
  • Slater, L.J., (1966) Generalized Hypergeometric Functions, , Cambridge: Cambridge University Press
  • Sturmfels, B., (1996) Gröbner Bases and Convex Polytopes, , Providence, RI: American Mathematical Society
  • Sturmfels, B., Trung, N.V., Vogel, W., Bounds on degrees of projective schemes (1995) Math. Ann., 302 (3), pp. 417-432


---------- APA ----------
Dickenstein, A., Matusevich, L.F. & Sadykov, T. (2005) . Bivariate hypergeometric D-modules. Advances in Mathematics, 196(1), 78-123.
---------- CHICAGO ----------
Dickenstein, A., Matusevich, L.F., Sadykov, T. "Bivariate hypergeometric D-modules" . Advances in Mathematics 196, no. 1 (2005) : 78-123.
---------- MLA ----------
Dickenstein, A., Matusevich, L.F., Sadykov, T. "Bivariate hypergeometric D-modules" . Advances in Mathematics, vol. 196, no. 1, 2005, pp. 78-123.
---------- VANCOUVER ----------
Dickenstein, A., Matusevich, L.F., Sadykov, T. Bivariate hypergeometric D-modules. Adv. Math. 2005;196(1):78-123.