The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kaehler manifold

Details The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kaehler manifold The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kaehler manifold

2005-02-22

arxiv.org/abs/math/0502451v5

Ann. Fac. Sci. Toulouse Math. (6), 16(1): 147-178, 2007

Mathematics

Complex Variables

22 pages; v3 Recast using Levi decomposition, proofs the same; v4 reference added; v5 introductory section & new example added

Scientific paper

The aim of this paper is to study the pro-algebraic fundamental group of a compact Kaehler manifold. Following work by Simpson, the structure of this group's pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.'s result on the de Rham fundamental group, and Goldman and Millson's result on deforming representations of Kaehler groups, and can be regarded as a consequence of formality of the schematic homotopy type. New examples are given of groups which cannot arise as Kaehler groups.

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