BPS cohomology for rank 2 degree 0 Higgs bundles (and more)

TL;DR

This paper presents a formula relating the E-series of rank 2 degree 0 Higgs bundle moduli stacks to intersection E-polynomials, supporting a conjecture on BPS cohomology with implications for non-abelian Hodge theory.

Contribution

It introduces a new formula connecting Higgs bundle moduli stacks and intersection cohomology, providing evidence for Davison's conjecture on BPS cohomology.

Findings

Formula comparing E-series and intersection E-polynomials

Evidence supporting Davison's conjecture on BPS cohomology

Applications to cohomological $\\chi$-independence tests

Abstract

We give a formula comparing the E-series of the moduli stacks of rank 2 degree 0 semistable Higgs bundles in genus $g \geq 2$ to intersection E-polynomials of its coarse moduli space. A parellel formula holds in various 2-Calabi-Yau settings, for example for sheaves on K3 surfaces, or preprojective algebras of $g$-loop quivers. As a consequence we provide evidence for a conjecture of Davison on the BPS cohomology of Higgs bundles, which has implications for non-abelian Hodge theory for stacks. We apply the formula to cohomological $\chi$-independence tests for BPS cohomology of Higgs bundles and K3 surfaces.