Unipotent flat bundles and Higgs bundles over compact Kahler manifolds

摘要

We characterize those unipotent representations of the fundamental group pi(1)( X, x) of a compact Kahler manifold X, which correspond to a Higgs bundle whose underlying Higgs field is equal to zero.The characterization is parallel to the one that R. Hain gave of those unipotent representations of pi(1)( X, x) that can be realized as the monodromy of a flat connection on the holomorphically trivial vector bundle.We see that Hain's result and ours follow from a careful study of Simpson's correspondence between Higgs bundles and local systems.