Wild nonabelian Hodge theory on curves

Olivier Biquard; Philip Boalch

Wild nonabelian Hodge theory on curves

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arxiv math/0111098 v3 pith:MC63VWSG submitted 2001-11-08 math.DG math.AG

Olivier Biquard , Philip Boalch This is my paper

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keywords connectionhiggsbundlescarrycompletecomplexconnectionscorrespondence

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On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. The moduli spaces of these objects are obtained by fixing at each singularity the polar part of the connection. We prove that they carry hyperKahler metrics, which are complete when the residue of the connection if semisimple.

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A stability-preserving map T from star-shaped Nakajima quiver varieties to central-Levi parabolic Higgs bundle moduli spaces is a homeomorphism on the trivial holomorphic structure locus and identifies their holomorph...

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