Projective Dual Varieties and General Discriminants

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


We denote by P n the standard complex projective space of dimension n. Thus a point of P n is given by (n + 1) homogeneous coordinates (x 0:...: x n ), x i ∈ C, which are not all equal to 0 and are regarded modulo simultaneous multiplication by a non-zero number. More generally, if V is a finite-dimensional complex vector space, then we denote by P(V) the projectivization of V, i.e., the set of 1-dimensional vector subspaces in V. Thus P n = P(C n+1).


Projective Space Projective Variety Dual Variety Smooth Point Projective Subspace 
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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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