DUALITY RELATING SPACES OF ALGEBRAIC COCYCLES AND CYCLES

In this paper a fundamental duality is established between algebraic c ycles and algebraic cocycles on a smooth projective variety. The proof makes use of a new Chow moving lemma for families. If X is a smooth p rojective variety of dimension n, our duality map induces isomorphisms L(s)H(k)(X) --> L(n-s)H(2n-k)(X) for 2s less than or equal to k which carry over via natural transformations to the Poincare duality isomor phism H-k(X;Z) --> H-2n-k(X;Z). More generally, for smooth projective varieties X and Y the natural graphing homomorphism sending algebraic cocycles on X with values in Y to algebraic cycles on the product X x Y is a weak homotopy equivalence. The main results have a wide variety of applications. Among these are the determination of the homotopy ty pe of certain algebraic mapping complexes and a computation of the gro up of algebraic s-cocycles module algebraic equivalence on a smooth pr ojective variety. Copyright (C) 1996 Elsevier Science Ltd