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

2004/03/08 by Boysal, Arzu, Kumar, Shrawan
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0403141

Abstract

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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