Cohomology of vector bundles on the moduli space of parabolic connections on ℙ¹ minus 5 points

2025/10/14 by Matsubara, Yuki
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.12578

Abstract

We study the moduli space of parabolic connections of rank two on the complex projective line ℙ¹ 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 ℙ¹. Moreover, we give an explicit geometric description of the compactification of this moduli space.

Citations

• Moduli of Higgs bundles over the five punctured sphere
• Parabolic Hecke eigensheaves
• On the Cohomology of Moduli Space of Parabolic Connections
• Autoduality of compactified Jacobians for curves with plane singularities
• Cohomology of line bundles on compactified Jacobians
• Higher direct images of Lagrangian fibrations

Related

• On the Cohomology of Moduli Space of Parabolic Connections
• Topology of moduli of parabolic connections with fixed determinant
• Line bundles on the moduli space of parabolic connections over a compact Riemann surface
• Recursive relations in the cohomology rings of moduli spaces of rank 2\n parabolic bundles on the Riemann sphere
• Generators for the moduli space of parabolic bundle