Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds

Details Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds

2003-05-18

arxiv.org/abs/math/0305258v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We characterize those unipotent representations of the fundamental group $\pi_1(X,x)$ 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 $\pi_1(X,x)$ 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.

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