On the motives of moduli of chains and Higgs bundles

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

2011-04-29

arxiv.org/abs/1104.5558v1

Mathematics

Algebraic Geometry

44 pages

Scientific paper

We take another approach to Hitchin's strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle-action. Our computation is done in the dimensional completion of the Grothendieck ring of varieties and starts by describing the classes of moduli stacks of chains rather than their coarse moduli spaces. As an application we show that the n-torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space of twisted SL_n-Higgs-bundles of degree coprime to n and we give an explicit formula for the motive of the moduli space of Higgs bundles of rank 4 and odd degree. This provides new evidence for a conjecture of Hausel and Rodr\'iguez-Villegas. Along the way we find explicit recursion formulas for the motives of several types of moduli spaces of stable chains.

Affiliated with

Also associated with

No associations

Rating

On the motives of moduli of chains and Higgs bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the motives of moduli of chains and Higgs bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the motives of moduli of chains and Higgs bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-17231