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Motives of moduli spaces of rank $ 3 $ vector bundles and Higgs bundles on a curve

  • Received: 16 February 2021 Revised: 01 November 2021 Accepted: 22 November 2021 Published: 09 December 2021
  • We prove formulas for the rational Chow motives of moduli spaces of semistable vector bundles and Higgs bundles of rank $ 3 $ and coprime degree on a smooth projective curve. Our approach involves identifying criteria to lift identities in (a completion of) the Grothendieck group of effective Chow motives to isomorphisms in the category of Chow motives. For the Higgs moduli space, we use motivic Białynicki-Birula decompositions associated with a scaling action, together with the variation of stability and wall-crossing for moduli spaces of rank $ 2 $ pairs, which occur in the fixed locus of this action.

    Citation: Lie Fu, Victoria Hoskins, Simon Pepin Lehalleur. Motives of moduli spaces of rank $ 3 $ vector bundles and Higgs bundles on a curve[J]. Electronic Research Archive, 2022, 30(1): 66-89. doi: 10.3934/era.2022004

    Related Papers:

  • We prove formulas for the rational Chow motives of moduli spaces of semistable vector bundles and Higgs bundles of rank $ 3 $ and coprime degree on a smooth projective curve. Our approach involves identifying criteria to lift identities in (a completion of) the Grothendieck group of effective Chow motives to isomorphisms in the category of Chow motives. For the Higgs moduli space, we use motivic Białynicki-Birula decompositions associated with a scaling action, together with the variation of stability and wall-crossing for moduli spaces of rank $ 2 $ pairs, which occur in the fixed locus of this action.



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