The Hilbert–Chow morphism and the incidence divisor: Zero-cycles and divisors

For a smooth projective variety X of dimension n, on the product of Chow varieties Ca(X)×Cn−a−1(X) parameterizing pairs (A,B) of an a-cycle A and an (n−a−1)-cycle B in X, Barry Mazur raised the problem of constructing a Cartier divisor supported on the locus of pairs with A∩B≠0̸. We introduce a new approach to this problem, and new techniques supporting this approach.