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

Abstract

We give a formula comparing the E-series of the moduli stacks of rank 2 degree 0 semistable Higgs bundles in genus g≥2 to intersection E-polynomials of its coarse moduli space. A parallel 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 χ-independence tests for BPS cohomology of Higgs bundles and K3 surfaces.