Two-step nilpotent monodromy of local systems on special varieties
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911573288681472 |
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| author | Cao, Junyan Deng, Ya Hacon, Christopher D. Paun, Mihai |
| author_facet | Cao, Junyan Deng, Ya Hacon, Christopher D. Paun, Mihai |
| contents | 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 Kähler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14539 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-step nilpotent monodromy of local systems on special varieties Cao, Junyan Deng, Ya Hacon, Christopher D. Paun, Mihai Algebraic Geometry 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 Kähler 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. |
| title | Two-step nilpotent monodromy of local systems on special varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.14539 |