Resultants and Chow Forms via Exterior Syzygies

  title={Resultants and Chow Forms via Exterior Syzygies},
  author={David Eisenbud and Jerzy Weyman},
Let W be a vector space of dimension n+ 1 over a field K. The Chow divisor of a k-dimensional variety X in P = P(W ) is the hypersurface, in the Grassmannian Gk+1 of planes of codimension k+1 in P, whose points (over the algebraic closure of K) are the planes that meet X . The Chow form of X is the defining equation of the Chow divisor. For example, the resultant of k+ 1 forms of degree e in k + 1 variables is the Chow form of P embedded by the e-th Veronese mapping in P with n = ( k+e k ) − 1… CONTINUE READING
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