Moduli of Parabolic Higgs Bundles and Atiyah Algebroids

Details Moduli of Parabolic Higgs Bundles and Atiyah Algebroids Moduli of Parabolic Higgs Bundles and Atiyah Algebroids

2008-11-06

arxiv.org/abs/0811.0817v3

J. reine angew. Math. 649 (2010), 89-116

Mathematics

Algebraic Geometry

34 pages. Some small edits, corrected minor mistake in proof of lemma 2.1. Added journal reference

Scientific paper

10.1515/CRELLE.2010.090

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-Ng\^o. We discuss the Hitchin system, and demonstrate that all these moduli spaces are integrable systems in the Poisson sense.

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