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2 results

  • Irreducible quotients of A-hypergeometric systems

  • Part of
  • Mutsumi Saito
  • Journal:
    Compositio Mathematica / Volume 147 / Issue 2 / March 2011
    Published online by Cambridge University Press:
    17 August 2010, pp. 613-632
    Print publication:
    March 2011
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  • Gel’fand, Kapranov and Zelevinsky proved, using the theory of perverse sheaves, that in the Cohen–Macaulay case an A-hypergeometric system is irreducible if its parameter vector is non-resonant. In this paper we prove, using the theory of the ring of differential operators on an affine toric variety, that in general an A-hypergeometric system is irreducible if and only if its parameter vector is non-resonant. In the course of the proof, we determine the irreducible quotients of an A-hypergeometric system.

  • Isomorphism Classes of A-Hypergeometric Systems

  • Mutsumi Saito
  • Journal:
    Compositio Mathematica / Volume 128 / Issue 3 / September 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 323-338
    Print publication:
    September 2001
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  • Given a finite set A of integral vectors and a parameter vector, Gel'fand, Kapranov, and Zelevinskii defined a system of differential equations, called an A-hypergeometric (or a GKZ hypergeometric) system. Classifying the parameters according to the D-isomorphism classes of their corresponding A-hypergeometric systems is one of the most fundamental problems in the theory. In this paper we give a combinatorial answer for the problem under the assumption that the finite set A lies in a hyperplane off the origin, and illustrate it in two particularly simple cases: the normal case and the monomial curve case.