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 μL-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. © Copyright 2009 Mathematical Sciences Publishers.