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 Bia lynicki-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.

On the Chow Theory of Projectivizations

“…See[17] for recent results in this direction about rational Chow motives; our results here might also be helpful in obtaining results for integral coefficients.…”