Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds

الأصل · EN

We characterize those unipotent representations of the fundamental group π₁(X,x) of a compact Kaehler 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 π₁(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.