Picard groups of the moduli spaces of semistable sheaves I

Abstract

We compute the Picard group of the moduli space $U^{\prime }$ of semistable vector bundles of rank $n$ and degree $d$ on an irreducible nodal curve $Y$ and show that $U^{\prime }$ is locally factorial. We determine the canonical line bundles of $U^{\prime }$ and $U_L^{\prime }$, the subvariety consisting of vector bundles with a fixed determinant. For rank 2, we compute the Picard group of other strata in the compactification of $U^{\prime }$.

16 pages, no figures, no tables