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Given a sheaf on a projective space P^n we define a sequence of canonical andeasily computable Chow complexes on the Grassmannians of planes in P^n,generalizing the Beilinson monad on P^n. If the sheaf has dimension k, then theChow form of the associated k-cycle is the determinant of the Chow complex onthe Grassmannian of planes of codimension k+1. Using the theory of vectorbundles and the canonical nature of the complexes we are able to give explicitdeterminantal and Pfaffian formulas for resultants in some cases where nopolynomial formulas were known. For example, the Horrocks-Mumford bundle givesrise to a polynomial formula for the resultant of five homogeneous forms ofdegree eight in five variables.

Resultants and Chow forms via exterior syzygies