Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T09:38:13.426Z Has data issue: false hasContentIssue false
  • English
  • Français

Moduli spaces of orthogonal and symplectic bundles over an algebraic curve

Part of: Representation theory of rings and algebras (Co)homology theory Curves 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: serman@math.unice.fr)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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