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

TL;DR

This paper presents a recursive algorithm to compute the cohomology of moduli spaces of Higgs bundles on curves and applies it to determine the y-genus of PGL_n-Higgs bundles, confirming a conjecture.

Contribution

It introduces a new recursive method for cohomology computation and calculates the y-genus for PGL_n-Higgs bundles, validating a prior conjecture.

Findings

Recursive algorithm for cohomology of Higgs moduli spaces

Explicit computation of y-genus for PGL_n-Higgs bundles

Confirmation of Hausel's conjecture on y-genus

Abstract

Building on our previous joint work with A. Schmitt [7] 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.