Principal A-Determinants

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


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.



Toric Variety Coherent Sheave Laurent Polynomial Characteristic Cycle Principal Determinant 
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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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