Kobayashi–Hitchin correspondence for tame harmonic bundles II

Mochizuki, Takuro¹

¹ Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Geometry & topology, Tome 13 (2009) no. 1, pp. 359-455.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.359

Keywords: harmonic bundle, $\lambda$-connection, Kobayashi–Hitchin correspondence

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