Rank 3 rigid representations of projective fundamental groups

Adrian Langer; Carlos Simpson

doi:10.1112/S0010437X18007182

Rank 3 rigid representations of projective fundamental groups

Algebraic Geometry 2019-02-20 v3

Authors: Adrian Langer , Carlos Simpson

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Abstract

Let X be a smooth complex projective variety with basepoint x. We prove that every rigid integral irreducible representation $\pi_1(X,x)\to SL (3,{\mathbb C})$ is of geometric origin, i.e., it comes from some family of smooth projective varieties. This partially generalizes an earlier result by K. Corlette and the second author in the rank 2 case and answers one of their questions.

Keywords

rigid representations projective fundamental groups geometric origin smooth projective varieties rank 3 integral irreducible representation SL(3,C)

Cite

@article{arxiv.1604.03252,
  title  = {Rank 3 rigid representations of projective fundamental groups},
  author = {Adrian Langer and Carlos Simpson},
  journal= {arXiv preprint arXiv:1604.03252},
  year   = {2019}
}

Comments

v3, 49 pages; final version, to appear in Compositio Math

Rank 3 rigid representations of projective fundamental groups

Abstract

Keywords

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