The Hilbert-Chow Morphism and the Incidence Divisor

For a smooth projective variety $P$ of dimension $n$, we construct a Cartier divisor supported on the incidence locus in the product of Chow varieties $\mathscr{C}_a (P) \times \mathscr{C}_{n -a - 1}(P)$. There is a natural definition of the corresponding line bundle on a product of Hilbert schemes, and we show this bundle descends to the Chow varieties. This answers a question posed by Barry Mazur.

2010 Mathematics Subject Classification: Primary 14C05

Keywords and Phrases: Chow variety, Hilbert scheme

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