Kobayashi–Hitchin correspondence for tame harmonic bundles II

Mochizuki, Takuro

doi:10.2140/gt.2009.13.359

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Kobayashi–Hitchin correspondence for tame harmonic bundles II

Takuro Mochizuki

Geometry & Topology 13 (2009) 359–455

DOI: 10.2140/gt.2009.13.359

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 $μ_{L}$ –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

Volume 13, issue 1 (2009)