Abstract
We study the moduli space of logarithmic connections of rank 2 on \({\mathbb {P}}^1 {\setminus } \{ t_1, \dots , t_5 \}\) with fixed spectral data. The aim of this paper is to compute the cohomology of this space, a computation that will be used to extend the results of the Geometric Langlands Correspondence due to D. Arinkin to the case where these types of connections have five simple poles on \({\mathbb {P}}^1\).
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06 February 2021
An Erratum to this paper has been published: https://doi.org/10.1007/s00229-020-01270-7
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Acknowledgements
I am very grateful to Professor Masa-Hiko Saito for his constant attention to this work and for warm encouragement. I also thank Doctor Arata Komyo for numerous stimulating discussions and Professor Frank Loray for his hospitality at Université de Rennes 1.
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Matsubara, Y. On the cohomology of the moduli space of parabolic connections. manuscripta math. 164, 593–604 (2021). https://doi.org/10.1007/s00229-019-01161-6
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DOI: https://doi.org/10.1007/s00229-019-01161-6