Volume 13, issue 1 (2009)

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Kobayashi–Hitchin correspondence for tame harmonic bundles II

Takuro Mochizuki

Geometry & Topology 13 (2009) 359–455
Abstract

Let X be a smooth irreducible projective complex variety with an ample line bundle L, and D be a simple normal crossing hypersurface. We establish the Kobayashi–Hitchin correspondence between tame harmonic bundles on X D and μL–stable parabolic λ–flat bundles with trivial characteristic numbers on (X,D). In particular, we obtain the quasiprojective version of the Corlette–Simpson correspondence between flat bundles and Higgs bundles.

Keywords
harmonic bundle, $\lambda$-connection, Kobayashi–Hitchin correspondence
Mathematical Subject Classification 2000
Primary: 14J60
Secondary: 53C07
References
Publication
Received: 11 February 2008
Revised: 26 September 2008
Accepted: 4 September 2008
Preview posted: 11 November 2008
Published: 1 January 2009
Proposed: Simon Donaldson
Seconded: Tom Mrowka, Ron Fintushel
Authors
Takuro Mochizuki
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan