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Rank 3 rigid representations of projective fundamental groups

Part of: Birational geometry (Co)homology theory Families, fibrations

Published online by Cambridge University Press:  30 May 2018

Adrian Langer  and
Carlos Simpson
Adrian Langer
Affiliation:
Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland email alan@mimuw.edu.pl
Carlos Simpson
Affiliation:
Laboratoire J. A. Dieudonné, CNRS UMR 7351, Université Côte d’Azur, 06108 Nice, Cedex 2, France email Carlos.SIMPSON@unice.fr
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Abstract

Let $X$ be a smooth complex projective variety with basepoint $x$ . We prove that every rigid integral irreducible representation $\unicode[STIX]{x1D70B}_{1}(X\!,x)\rightarrow \operatorname{SL}(3,\mathbb{C})$ is of geometric origin, i.e., it comes from some family of smooth projective varieties. This partially generalizes an earlier result by Corlette and the second author in the rank 2 case and answers one of their questions.

Keywords

fundamental groupcomplex varietiesrigid representationcomplex variation of Hodge structure

MSC classification

Primary: 14F35: Homotopy theory; fundamental groups
Secondary: 14D06: Fibrations, degenerations 14D07: Variation of Hodge structures 14E20: Coverings
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 7 , July 2018 , pp. 1534 - 1570
Copyright
© The Authors 2018 

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