Picard groups of the moduli spaces of semistable sheaves I

Usha N Bhosle

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Picard groups of the moduli spaces of semistable sheaves I

Usha N Bhosle

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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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Usha N Bhosle. 2004-06-28. Picard groups of the moduli spaces of semistable sheaves I. https://arxiv.org/abs/math/0406565

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