Explicit Determination of the Picard Group of Moduli Spaces of Semi-Stable G-Bundles on Curves

Details Explicit Determination of the Picard Group of Moduli Spaces of Semi-Stable G-Bundles on Curves Explicit Determination of the Picard Group of Moduli Spaces of Semi-Stable G-Bundles on Curves

2004-03-08

arxiv.org/abs/math/0403141v2

Mathematics

Algebraic Geometry

22 pages; final version

Scientific paper

Let $\mathcal C$ be a smooth irreducible projective curve over the complex numbers and let $G$ be a simple simply-connected complex algebraic group. Let $\mathfrak M=\mathfrak M(G,\mathcal C)$ be the moduli space of semistable principal $G$-bundles on $\mathcal C$. By an earlier result of Kumar-Narasimhan, the Picard group of $\mathfrak M$ is isomorphic with the group of integers. However, in their work the generator of the Picard group was not determined explicitly. The aim of this paper to give the generator `explicitly.' The proof involves an interesting mix of geometry and topology.

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