English

The Hilbert-Chow morphism and the incidence divisor

Algebraic Geometry 2010-09-30 v1

Abstract

For a smooth projective variety PP, we construct a Cartier divisor supported on the incidence locus in Ca(P)×Cdim(P)a1(P)\mathscr{C}_a (P) \times \mathscr{C}_{\dim(P)-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 Mazur.

Keywords

Cite

@article{arxiv.1009.5898,
  title  = {The Hilbert-Chow morphism and the incidence divisor},
  author = {Joseph Ross},
  journal= {arXiv preprint arXiv:1009.5898},
  year   = {2010}
}
R2 v1 2026-06-21T16:21:01.444Z