JournalsjemsVol. 16, No. 12pp. 2617–2668

On the motives of moduli of chains and Higgs bundles

  • Oscar García-Prada

    Universidad Autónoma de Madrid, Spain
  • Jochen Heinloth

    Universität Duisburg-Essen, Germany
  • Alexander H. W. Schmitt

    Freie Universität Berlin, Germany
On the motives of moduli of chains and Higgs bundles cover
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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 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 nn-torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space of twisted SLn_n-Higgs bundles of degree coprime to nn 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 Rodríguez-Villegas. Along the way we find explicit recursion formulas for the motives of several types of moduli spaces of stable chains.

Cite this article

Oscar García-Prada, Jochen Heinloth, Alexander H. W. Schmitt, On the motives of moduli of chains and Higgs bundles. J. Eur. Math. Soc. 16 (2014), no. 12, pp. 2617–2668

DOI 10.4171/JEMS/494