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Rank 3 rigid representations of projective fundamental groups
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 7 / July 2018
- Published online by Cambridge University Press:
- 30 May 2018, pp. 1534-1570
- Print publication:
- July 2018
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- Article
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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.
