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Pseudo-real principal Higgs bundles on compact Kähler manifolds

Indranil Biswas; Oscar García-Prada; Jacques Hurtubise — 2014

Annales de l’institut Fourier

Let $X$ be a compact connected Kähler manifold equipped with an anti-holomorphic involution which is compatible with the Kähler structure. Let $G$ be a connected complex reductive affine algebraic group equipped with a real form $σ_{G}$ . We define pseudo-real principal $G$ -bundles on $X$ . These are generalizations of real algebraic principal $G$ -bundles over a real algebraic variety. Next we define stable, semistable and polystable pseudo-real principal $G$ -bundles. Their relationships with the usual stable, semistable...

On the motives of moduli of chains and Higgs bundles

Oscar García-Prada; Jochen Heinloth; Alexander Schmitt — 2014

Journal of the European Mathematical Society

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...

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