Geometric local systems on very general curves and isomonodromy
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916621719699456 |
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| author | Landesman, Aaron Litt, Daniel |
| author_facet | Landesman, Aaron Litt, Daniel |
| contents | We show that the minimum rank of a non-isotrivial local system of geometric origin, on a suitably general $n$-pointed curve of genus $g$, is at least $2\sqrt{g+1}$. We apply this result to resolve conjectures of Esnault-Kerz and Budur-Wang. The main input is an analysis of stability properties of flat vector bundles under isomonodromic deformation, which additionally answers questions of Biswas, Heu, and Hurtubise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_00039 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometric local systems on very general curves and isomonodromy Landesman, Aaron Litt, Daniel Algebraic Geometry Complex Variables We show that the minimum rank of a non-isotrivial local system of geometric origin, on a suitably general $n$-pointed curve of genus $g$, is at least $2\sqrt{g+1}$. We apply this result to resolve conjectures of Esnault-Kerz and Budur-Wang. The main input is an analysis of stability properties of flat vector bundles under isomonodromic deformation, which additionally answers questions of Biswas, Heu, and Hurtubise. |
| title | Geometric local systems on very general curves and isomonodromy |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2202.00039 |