On the motives of moduli of chains and Higgs bundles
Abstract
We take another approach to Hitchin's strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circleaction. 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 ntorsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space of twisted SL_nHiggsbundles 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 RodríguezVillegas. Along the way we find explicit recursion formulas for the motives of several types of moduli spaces of stable chains.
 Publication:

arXiv eprints
 Pub Date:
 April 2011
 DOI:
 10.48550/arXiv.1104.5558
 arXiv:
 arXiv:1104.5558
 Bibcode:
 2011arXiv1104.5558G
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 44 pages