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Rank 3 rigid representations of projective fundamental groups
Published online by Cambridge University Press: 30 May 2018
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.
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- Research Article
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- © The Authors 2018
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