Picard groups of the moduli spaces of semistable sheaves I

Details Picard groups of the moduli spaces of semistable sheaves I Picard groups of the moduli spaces of semistable sheaves I

2004-06-28

arxiv.org/abs/math/0406565v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 2, May 2004, pp. 107-122

Mathematics

Algebraic Geometry

16 pages, no figures, no tables

Scientific paper

We compute the Picard group of the moduli space $U'$ of semistable vector bundles of rank $n$ and degree $d$ on an irreducible nodal curve $Y$ and show that $U'$ is locally factorial. We determine the canonical line bundles of $U'$ and $U'_L$, 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 $U'$.

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