#### 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 ${\mu }_{L}$–stable parabolic $\lambda$–flat bundles with trivial characteristic numbers on $\left(X,D\right)$. 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
Primary: 14J60
Secondary: 53C07
##### 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