Moduli of parabolic Higgs bundles and Atiyah algebroids

Marina Logares, Johan Martens

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study the geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points. We show that this space possesses a Poisson structure, extending the one on the dual of an Atiyah algebroid over the moduli space of parabolic vector bundles. By considering the case of full flags, we get a Grothendieck-Springer resolution for all other flag types, in particular for the moduli spaces of twisted Higgs bundles, as studied by Markman and Bottacin and used in the recent work of Laumon-Ngo. We discuss the Hitchin system, and demonstrate that all these moduli spaces are integrable systems in the Poisson sense.

Original languageEnglish
Pages (from-to)89-116
Number of pages28
JournalJournal für die reine und angewandte Mathematik
Volume2010
Issue number649
DOIs
Publication statusPublished - Dec 2010

Keywords

  • MANIFOLDS
  • INTEGRABLE SYSTEMS
  • VECTOR-BUNDLES
  • SHEAVES
  • RIEMANN SURFACE
  • PAIRS
  • SPACES
  • THEOREM
  • EQUATIONS
  • SPECTRAL CURVES

Cite this