Associated Varieties and General Resultants

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


The Grassmann variety (or Grassmannian) G(k, n) is the set of all k-dimensional vector subspaces in C n . For k = 1, this is the projective space P n−1. Since vector subspaces in C n correspond to projective subspaces in P n−1, we see that G(k, n) parametrizes (k−1)-dimensional projective subspaces in P n−1. In a more invariant fashion, we can start from any finite-dimensional vector space V and construct the Grassmannian G(k, V) of k-dimensional vector subspaces in V.


Vector Bundle Line Bundle Projective Space Spectral Sequence 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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