Generators for the cohomology of the moduli space of irregular parabolic Higgs bundles

2024/02/08 by Lee, Jia Choon, Lee, Sukjoo
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.05380

Abstract

We prove that the pure part of the cohomology ring of the moduli space of irregular \underlineξ-parabolic Higgs bundles is generated by the Künneth components of the Chern classes of a universal bundle and the Chern classes of the successive quotients of a universal flag of subbundles. As an application, in the regular full-flag case, we demonstrate a similar result for the cohomology ring of the moduli spaces of parabolic and strongly parabolic Higgs bundles.

Related

• Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles
• Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles
• Hodge structure on the cohomology of the moduli space of Higgs bundles
• Two-dimensional moduli spaces of irregular Higgs bundles
• Hyperpolygon spaces and moduli spaces of parabolic Higgs bundles