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

Abstract

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 Bialynicki-Birula decompositions associated to a scaling action with variation of stability and wall-crossing for moduli spaces of rank 2 pairs, which occur in the fixed locus of this action.

Final version appearing in a special issue "Birational geometry and moduli of projective varieties" of the Electronic Research Archive

References in corpus (1)

• Motivic decompositions of moduli spaces of vector bundles on curves

Cited by in corpus (1)

• Motivic mirror symmetry and $\chi$-independence for Higgs bundles in arbitrary characteristic