The Cayley Method for Studying Discriminants

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


In Chapter 1 we introduced, for any projective variety XP n , the X-discriminant Δ X which is the equation of the projective dual variety X (so Δ X is a constant if X is not a hypersurface). We now explain the method that allows us, for a smooth X, to write down at least in principle, the polynomial Δ X . The method goes back to the remarkable paper by Cayley [Ca4] on elimination theory, in which the foundations were laid for what is now called homological algebra. The Cayley method can also be applied to other similar problems, such as finding resultants (see Chapter 3).


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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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