Rank 3 rigid representations of projective fundamental groups
Résumé
Let $X$ be a smooth complex projective variety with basepoint $x$.
We prove that every rigid integral irreducible representation $\pi_1(X ,x)\to SL (3, C)$
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.