Rank 3 rigid representations of projective fundamental groups

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.

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

References in corpus (1)

• Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

Cited by in corpus (3)

• Absolute sets and the Decomposition Theorem
• Absolute sets of rigid local systems
• On smooth projective D-affine varieties