Picard groups of Hilbert schemes of curves

Abstract

We calculate the Picard group, over the integers, of the Hilbert scheme of smooth, irreducible, non-degenerate curves of degree $d$and genus $g\ge 4$ in ${\mathbb{P}}^r$, in the case when $d\ge 2g+1$ and $r\le d-g$. We express the classes of the generators in terms of some ``natural'' divisor classes.

arXiv comment13 pages, LaTeX