On the motives of moduli of parabolic chains and parabolic Higgs bundles

Analogous to the Higgs bundles on a Riemann surface which played an important role in the study of representations of the fundamental group of the surface, the parabolic Higgs bundles play also their importance in the study of the fundamental group but of the punctured surface. In this paper, we give an algorithm to calculate the (virtual) motive (i.e. in a suitable Grothendieck group) of the moduli spaces of parabolic Higgs bundles of fixed rank and fixed parabolic structure, using localization with respect to the circle action. (c) 2024 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.