Orbifold Riemann Surfaces and the Yang-Mills-Higgs Equations

Abstract

We extend Hitchin's results on "The self-duality equations on a Riemann surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove existence results for orbifold solutions of the Yang-Mills-Higgs equations and construct the moduli space of solutions. These moduli spaces provide interesting examples of non-compact hyper-Kahler manifolds in all dimensions divisible by 4 and of completely integrable Hamiltonian systems. We also reinterpret these moduli spaces as spaces of orbifold Higgs bundles and as representation varieties of Fuchsian groups.

Hard copies are available on request. This paper will appear in the "Annali della Scuola Normale Superiore di Pisa (classe di scienze)". LaTeX2.09 with AMS fonts

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