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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Unipotent flat bundles and Higgs bundles over compact Kähler manifolds


Author: Silke Lekaus
Journal: Trans. Amer. Math. Soc. 357 (2005), 4647-4659
MSC (2000): Primary 14F05, 14C30, 32Q20
Published electronically: December 28, 2004
MathSciNet review: 2156725
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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.


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Additional Information

Silke Lekaus
Affiliation: Fachbereich 6 - Mathematik, Universität Essen, 45117 Essen, Germany
Email: silke.lekaus@uni-essen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03652-9
PII: S 0002-9947(04)03652-9
Received by editor(s): October 31, 2003
Received by editor(s) in revised form: January 24, 2004
Published electronically: December 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society