Derivative of the Riemann-Hilbert map
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914857594388480 |
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| author | Marković, Vladimir Tošić, Ognjen |
| author_facet | Marković, Vladimir Tošić, Ognjen |
| contents | Given a pair $(X,\nabla)$, consisting of a closed Riemann surface $X$ and a holomorphic connection $\nabla$ on the trivial principal bundle $X\times\mathrm{SL}_2(\mathbb{C})\to X$, the Riemann-Hilbert map sends $(X,\nabla)$ to its monodromy representation. We compute the derivative of this map, and provide a simple description of the locus where it is injective, recovering in the process several previously obtained results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivative of the Riemann-Hilbert map Marković, Vladimir Tošić, Ognjen Algebraic Geometry Complex Variables Differential Geometry Given a pair $(X,\nabla)$, consisting of a closed Riemann surface $X$ and a holomorphic connection $\nabla$ on the trivial principal bundle $X\times\mathrm{SL}_2(\mathbb{C})\to X$, the Riemann-Hilbert map sends $(X,\nabla)$ to its monodromy representation. We compute the derivative of this map, and provide a simple description of the locus where it is injective, recovering in the process several previously obtained results. |
| title | Derivative of the Riemann-Hilbert map |
| topic | Algebraic Geometry Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2407.03296 |