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arXiv · 2603.14539

Two-step nilpotent monodromy of local systems on special varieties

Junyan Cao·Ya Deng·Christopher D. Hacon·Mihai Paun
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Abstract

Let $X$ be a smooth complex quasi-projective variety that is special in the sense of Campana. We prove that the monodromy group of any complex local system on $X$ is virtually nilpotent of class at most $2$. This result sharply refines a theorem of Cadorel, Yamanoi, and the second author. To establish this result, we develop a deformation theory for certain local systems on quasi-compact K\"ahler manifolds by constructing universal deformations for such local systems. As a byproduct of our argument, we also show that a general fiber of the quasi-Albanese map of $X$ is special, extending a result of Campana and Claudon from the projective to the quasi-projective setting.

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Junyan Cao, Ya Deng, Christopher D. Hacon, Mihai Paun. 2026-03-15. Two-step nilpotent monodromy of local systems on special varieties. https://arxiv.org/abs/2603.14539

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