The Hilbert-Chow morphism and the incidence divisor -- Joe Ross, March 13, 2009

Let X be a smooth projective variety of dimension n, and let a,b be nonnegative integers such that a+b+1=n. I will discuss the locus of intersecting cycles inside the product of Chow varieties Ch_a(X) x Ch_b(X). In particular I will show the incidence locus is a Cartier divisor when a=b=1 and when a=0, b arbitrary. The main idea is to descend a line bundle from the corresponding product of Hilbert schemes. A new characterization of seminormal schemes plays a role in both defining the descent datum and showing it is effective.