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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Unipotent flat bundles and Higgs bundles over compact Kähler manifolds
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by Silke Lekaus PDF
Trans. Amer. Math. Soc. 357 (2005), 4647-4659 Request permission

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
  • 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