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

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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.