Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich.
mehr Informationen...
On the motives of moduli of chains and Higgs bundles
Ist Teil von
Journal of the European Mathematical Society : JEMS, 2014-01, Vol.16 (12), p.2617-2668
Ort / Verlag
Zuerich, Switzerland: European Mathematical Society Publishing House
Erscheinungsjahr
2014
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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 Rodríguez-Villegas. Along the way we find explicit recursion formulas for the motives of several types of moduli spaces of stable chains.