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Moduli spaces of orthogonal and symplectic bundles over an algebraic curve

Part of: Curves (Co)homology theory Representation theory of rings and algebras Algebraic groups

Published online by Cambridge University Press:  01 May 2008

Olivier Serman
Olivier Serman*
Affiliation:
Laboratoire J.-A. Dieudonné, UMR 6621 du CNRS, Université de Nice, Parc Valrose, F-06108 Nice cedex 02, France (email: [email protected])
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Abstract

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We prove that, given a smooth projective curve C of genus g≥2, the forgetful morphism (respectively ) from the moduli space of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles over C is an embedding. Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.

Keywords

moduli spacesorthogonal bundlessymplectic bundlesrepresentations of quivers

MSC classification

Secondary: 14H60: Vector bundles on curves and their moduli 14F05: Sheaves, derived categories of sheaves and related constructions 14L30: Group actions on varieties or schemes (quotients) 16G20: Representations of quivers and partially ordered sets
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 3 , May 2008 , pp. 721 - 733
Copyright
Copyright © Foundation Compositio Mathematica 2008