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On motives of parabolic Higgs bundles and parabolic connections

Indian Statistical Institute, Kolkata 700108, India

This work was done when the author was affiliated with Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Korea.

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https://doi.org/10.1142/S1664360724500012Cited by:0 (Source: Crossref)

Abstract

Let $X$ $X$ be a compact Riemann surface of genus $g \geq 2$ $g \geq 2$ and let $D \subset X$ $D \subset X$ be a fixed finite subset. We considered the moduli spaces of parabolic Higgs bundles and of parabolic connections over $X$ $X$ with the parabolic structure over $D$ $D$ . For generic weights, we showed that these two moduli spaces have equal Grothendieck motivic classes and their $E$ $E$ -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 $E$ $E$ -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.

Communicated by S. K. Jain

Keywords:

AMSC: 14C15, 14C30, 14D20, 14D23, 70G45

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Vol. 14, No. 02

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History

Received 2 September 2022

Revised 2 December 2023

Accepted 28 February 2024

Published: 25 March 2024

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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On motives of parabolic Higgs bundles and parabolic connections

Abstract

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