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The Picard group of the moduli of $G$-bundles on a curve

Published online by Cambridge University Press:  04 December 2007

ARNAUD BEAUVILLE ,
YVES LASZIO  and
CHRISTOPH SORGER
ARNAUD BEAUVILLE
Affiliation:
DMI – École Normale Supérieure, (URA 762 du CNRS), 45 rue d‘Ulm, F-75230 Paris Cedex 05, France. e-mail: beauville@dmi.ens.fr
YVES LASZIO
Affiliation:
DMI – École Normale Supérieure, (URA 762 du CNRS), 45 rue d‘Ulm, F-75230 Paris Cedex 05, France. e-mail: beauville@dmi.ens.fr
CHRISTOPH SORGER
Affiliation:
Institut de Mathématiques de Jussieu, (UMR 9994 du CNRS), Univ. Paris 7 – Case Postale 7012, 2 Place Jussieu, F-75251 Paris Cedex 05, France. e-mail: ssorger@math.jussien.fr
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Abstract

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Let G be a complex semi-simple group, and X a compact Riemann surface. The moduli space of principal G-bundles on X, and in particular the holomorphic line bundles on this space and their global sections, play an important role in the recent applications of Conformal Field Theory to algebraic geometry. In this paper we determine the Picard group of this moduli space when G is of classical or G$_2$ type (we consider both the coarse moduli space and the moduli stack).

Keywords

Principal bundlesmoduli spacesdeterminant bundle.
Type
Research Article
Information
Compositio Mathematica , Volume 112 , Issue 2 , June 1998 , pp. 183 - 216
Copyright
© 1998 Kluwer Academic Publishers