Kobayashi–Hitchin correspondence for tame harmonic bundles II

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.