Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds

Silke Lekaus

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arXiv · math/0305258

Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds

Silke Lekaus

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Abstract

We characterize those unipotent representations of the fundamental group $π_1(X,x)$ 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 $π_1(X,x)$ 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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BibTeX RIS

Silke Lekaus. 2003-05-18. Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds. https://arxiv.org/abs/math/0305258

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