Cohomology of vector bundles on the moduli space of parabolic connections on $\mathbb{P}^1$ minus $5$ points

Yuki Matsubara

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arXiv · 2510.12578

Cohomology of vector bundles on the moduli space of parabolic connections on $\mathbb{P}^1$ minus $5$ points

Yuki Matsubara

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Abstract

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.

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BibTeX RIS

Yuki Matsubara. 2025-10-14. Cohomology of vector bundles on the moduli space of parabolic connections on $\mathbb{P}^1$ minus $5$ points. https://arxiv.org/abs/2510.12578

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