Cohomology of vector bundles on the moduli space of parabolic connections on $\mathbb{P}^1$ minus $5$ points
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911291423064064 |
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| author | Matsubara, Yuki |
| author_facet | Matsubara, Yuki |
| contents | We study the moduli space of parabolic connections of rank two on the complex projective line $\mathbb{P}^1$ minus five points with fixed spectral data. This paper aims to compute the cohomology of the structure sheaf and a certain vector bundle on this space. We use this computation to extend the results of Arinkin, which proved a specific Geometric Langlands Correspondence to the case where these connections have five simple poles on $\mathbb{P}^1$. Moreover, we give an explicit geometric description of the compactification of this moduli space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12578 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomology of vector bundles on the moduli space of parabolic connections on $\mathbb{P}^1$ minus $5$ points Matsubara, Yuki Algebraic Geometry We study the moduli space of parabolic connections of rank two on the complex projective line $\mathbb{P}^1$ minus five points with fixed spectral data. This paper aims to compute the cohomology of the structure sheaf and a certain vector bundle on this space. We use this computation to extend the results of Arinkin, which proved a specific Geometric Langlands Correspondence to the case where these connections have five simple poles on $\mathbb{P}^1$. Moreover, we give an explicit geometric description of the compactification of this moduli space. |
| title | Cohomology of vector bundles on the moduli space of parabolic connections on $\mathbb{P}^1$ minus $5$ points |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2510.12578 |