Associated Varieties and General Resultants
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.
KeywordsVector Bundle Line Bundle Projective Space Spectral Sequence Projective Subspace
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