Twisted Higgs bundles and the fundamental group of compact Kähler manifolds

2000/09/08 by O. Garcia-Prada, S. Ramanan
Mathematics · #math.AG #msc:14D20 #msc:14F05 #msc:53C07

paper · pdf

published as Mathematical Research Letters, 2000 · 18 pages, no figures, Latex

arxiv created 2000/09/08 · arxiv updated 2009/11/30

Abstract

We study polystable Higgs bundles twisted by a line bundle over a compact Kähler 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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