Twisted Higgs bundles and the fundamental group of compact Kähler manifolds

Details Twisted Higgs bundles and the fundamental group of compact Kähler manifolds Twisted Higgs bundles and the fundamental group of compact Kähler manifolds

2000-09-08

arxiv.org/abs/math/0009093v1

Mathematical Research Letters, 2000

Mathematics

Algebraic Geometry

18 pages, no figures, Latex

Scientific paper

We study polystable Higgs bundles twisted by a line bundle over a compact K\"ahler manifold. These form a Tannakian category when the first and second Chern classes of the bundle are zero. In this paper we identify the corresponding Tannaka group in the case in which the line bundle is of finite order. This group is described in terms of the pro-reductive completion of the fundamental group of the manifold, and the character associated to the line bundle.

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