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.