Picard groups of the moduli spaces of semistable sheaves I

2004/06/28 by Usha N Bhosle
Mathematics · #math.AG #msc:14H60 #msc:14C22 #msc:14F05

paper · pdf

published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 2, May 2004, pp. 107-122 · 16 pages, no figures, no tables

arxiv created 2004/06/28 · arxiv updated 2009/12/01

Abstract

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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