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Principal A-Determinants

  • Israel M. Gelfand
  • Mikhail M. Kapranov
  • Andrei V. Zelevinsky
Part of the Mathematics: Theory & Applications book series (MBC)

Abstract

Our aim in this and in the following chapter is to study the Newton polytope of the A-discriminant Δ A . This will be done through an intermediary object, the so-called principal A-determinant E A . Like the A-discriminant, E A = E A (f) is a polynomial function in coefficients a ω of an indeterminate polynomial f ∈ C A . We shall do the following:
  1. (1)

    give a complete description of the Newton polytope of E A . It turns out to coincide with the secondary polytope Σ(A) (see Chapter 7);

     
  2. (2)

    give a formula (prime factorization) expressing E A as a product of Δ A and discriminants corresponding to some subsets of A;

     
  3. (3)

    give a formula for the product of values of a polynomial at its critical points in terms of the principal A-determinants.

     

Keywords

Toric Variety Coherent Sheave Laurent Polynomial Characteristic Cycle Principal Determinant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Israel M. Gelfand
    • 1
  • Mikhail M. Kapranov
    • 2
  • Andrei V. Zelevinsky
    • 3
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA
  3. 3.Department of MathematicsNortheastern UniversityBostonUSA

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