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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Sadykov, T M and Tanabé, S 2016. Maximally reducible monodromy of bivariate hypergeometric systems. Izvestiya: Mathematics, Vol. 80, Issue. 1, p. 221.


    Садыков, Тимур Мрадович Sadykov, Timur Mradovich Танабэ, Сусуму and Tanabe, S 2016. Максимально приводимая монодромия двумерных гипергеометрических систем. Известия Российской академии наук. Серия математическая, Vol. 80, Issue. 1, p. 235.


    D'Andrea, C. and Sombra, M. 2015. A Poisson formula for the sparse resultant. Proceedings of the London Mathematical Society, Vol. 110, Issue. 4, p. 932.


    Borisov, Lev A. and Paul Horja, R. 2013. On the better behaved version of the GKZ hypergeometric system. Mathematische Annalen, Vol. 357, Issue. 2, p. 585.


    Cattani, Eduardo Cueto, María Angélica Dickenstein, Alicia Di Rocco, Sandra and Sturmfels, Bernd 2013. Mixed discriminants. Mathematische Zeitschrift, Vol. 274, Issue. 3-4, p. 761.


    Cattani, E. Dickenstein, A. and Rodriguez Villegas, F. 2010. The Structure of Bivariate Rational Hypergeometric Functions. International Mathematics Research Notices,


    Esterov, A. 2010. Newton Polyhedra of Discriminants of Projections. Discrete & Computational Geometry, Vol. 44, Issue. 1, p. 96.


    Sadykov, T. M. 2008. Hypergeometric systems of equations with maximally reducible monodromy. Doklady Mathematics, Vol. 78, Issue. 3, p. 880.


    Curran, Raymond and Cattani, Eduardo 2007. Restriction of <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>A</mml:mi></mml:math>-discriminants and dual defect toric varieties. Journal of Symbolic Computation, Vol. 42, Issue. 1-2, p. 115.


    Borisov, Lev A. and Horja, R. Paul 2006. Mellin–Barnes integrals as Fourier–Mukai transforms. Advances in Mathematics, Vol. 207, Issue. 2, p. 876.


    Ressayre, N. 2005. Balanced Configurations of 2n + 1 Plane Vectors. Journal of Algebraic Combinatorics, Vol. 21, Issue. 3, p. 281.


    Dickenstein, Alicia and Sturmfels, Bernd 2002. Elimination Theory in Codimension 2. Journal of Symbolic Computation, Vol. 34, Issue. 2, p. 119.


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Rational Hypergeometric Functions

  • Eduardo Cattani (a1), Alicia Dickenstein (a2) and Bernd Sturmfels (a3)
  • DOI: http://dx.doi.org/10.1023/A:1017541231618
  • Published online: 01 September 2001
Abstract

Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors projectively dual to torus orbit closures. We show that most of these potential denominators never appear in rational hypergeometric functions. We conjecture that the denominator of any rational hypergeometric function is a product of resultants, that is, a product of special discriminants arising from Cayley configurations. This conjecture is proved for toric hypersurfaces and for toric varieties of dimension at most three. Toric residues are applied to show that every toric resultant appears in the denominator of some rational hypergeometric function.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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