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

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Abstract

The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler 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 Kähler 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 Kähler groups.
Original languageEnglish
Pages (from-to)147-178
JournalAnnales de la Faculte des Sciences de Toulouse
Volume16
Issue number1
DOIs
Publication statusPublished - 2007

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