Big monodromy for higher Prym representations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915547057225728 |
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| author | Landesman, Aaron Litt, Daniel Sawin, Will |
| author_facet | Landesman, Aaron Litt, Daniel Sawin, Will |
| contents | Let $Σ_{g'}\to Σ_g$ be a cover of an orientable surface of genus g by an orientable surface of genus g', branched at n points, with Galois group H. Such a cover induces a virtual action of the mapping class group $\text{Mod}_{g,n+1}$ of a genus g surface with n+1 marked points on $H^1(Σ_{g'}, \mathbb{C})$. When g is large in terms of the group H, we calculate precisely the connected monodromy group of this action. The methods are Hodge-theoretic and rely on a "generic Torelli theorem with coefficients." |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Big monodromy for higher Prym representations Landesman, Aaron Litt, Daniel Sawin, Will Algebraic Geometry Geometric Topology 14D05, 57K20, 14C30, 14C34 Let $Σ_{g'}\to Σ_g$ be a cover of an orientable surface of genus g by an orientable surface of genus g', branched at n points, with Galois group H. Such a cover induces a virtual action of the mapping class group $\text{Mod}_{g,n+1}$ of a genus g surface with n+1 marked points on $H^1(Σ_{g'}, \mathbb{C})$. When g is large in terms of the group H, we calculate precisely the connected monodromy group of this action. The methods are Hodge-theoretic and rely on a "generic Torelli theorem with coefficients." |
| title | Big monodromy for higher Prym representations |
| topic | Algebraic Geometry Geometric Topology 14D05, 57K20, 14C30, 14C34 |
| url | https://arxiv.org/abs/2401.13906 |