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Wild non-abelian Hodge theory on curves

Published online by Cambridge University Press:  04 December 2007

Olivier Biquard  and
Philip Boalch
Olivier Biquard
Affiliation:
IRMA, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, Franceolivier.biquard@math.u-strasbg.fr
Philip Boalch
Affiliation:
DMA, Ecole Normale Supérieure et CNRS, 45 rue d'Ulm, 75230 Paris Cedex 05, Franceboalch@dma.ens.fr
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Abstract

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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. Moduli spaces of these objects are obtained with fixed generic polar parts at each singularity, which amounts to fixing a coadjoint orbit of the group $GL_r(\mathbb{C}[z]/z^n)$. We prove that they carry complete hyper-Kähler metrics.

Keywords

Hermitian Einstein metricsintegrable connectionsirregular singularitiesmeromorphic Higgs bundles53C0734M55
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 1 , January 2004 , pp. 179 - 204
Copyright
Foundation Compositio Mathematica 2004