On motives of parabolic Higgs bundles and parabolic connections

Article Type

Research Article

Publication Title

Bulletin of Mathematical Sciences

Abstract

Let X be a compact Riemann surface of genus g ≥ 2 and let D ⊂ X be a fixed finite subset. We considered the moduli spaces of parabolic Higgs bundles and of parabolic connections over X with the parabolic structure over D. For generic weights, we showed that these two moduli spaces have equal Grothendieck motivic classes and their E-polynomials are the same. We also show that the Voevodsky and Chow motives of these two moduli spaces are also equal. We showed that the Grothendieck motivic classes and the E-polynomials of parabolic Higgs moduli and of parabolic Hodge moduli are closely related. Finally, we considered the moduli spaces with fixed determinants and showed that the above results also hold for the fixed determinant case.

DOI

10.1142/S1664360724500012

Publication Date

8-1-2024

Comments

Open Access; Gold Open Access; Green Open Access

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