The y -genus of the moduli space of PGL n -Higgs bundles on a curve (for degree coprime to n )

Abstract

Building on our previous joint work with A. Schmitt, we explain a recursive algorithm to determine the cohomology of moduli spaces of Higgs bundles on any given curve (in the coprime situation). As an application of the method, we compute the $y$-genus of the space of ${PGL}_n$-Higgs bundles for any rank $n$, confirming a conjecture of T. Hausel.