# Kobayashi-Hitchin correspondence for tame harmonic bundles II

Research paper by Takuro Mochizuki

Indexed on: 10 Feb '08Published on: 10 Feb '08Published in: Mathematics - Differential Geometry

#### Abstract

Let $X$ be a smooth projective complex variety with an ample line bundle $L$, and let $D$ be a simple normal crossing divisor. 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 $(X,D)$. Especially, we obtain the quasiprojective version of the Corlette-Simpson correspondence between flat bundles and Higgs bundles.