Unipotent flat bundles and Higgs bundles over compact Kähler manifolds
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Abstract:
We characterize those unipotent representations of the fundamental group $\pi _1(X,x)$ of a compact Kähler 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.References
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Additional Information
- Silke Lekaus
- Affiliation: Fachbereich 6 - Mathematik, Universität Essen, 45117 Essen, Germany
- Email: silke.lekaus@uni-essen.de
- Received by editor(s): October 31, 2003
- Received by editor(s) in revised form: January 24, 2004
- Published electronically: December 28, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 4647-4659
- MSC (2000): Primary 14F05, 14C30, 32Q20
- DOI: https://doi.org/10.1090/S0002-9947-04-03652-9
- MathSciNet review: 2156725