2023/09/13 by Sumit Roy, Roy, Sumit
Mathematics · #14C15 #14C30 #14D20 #14D23 #70G45 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2309.06967
openalex publication_date 2023/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.