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arXiv · 2201.09962

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

Sebastian Schlegel Mejia
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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 $χ$-independence tests for BPS cohomology of Higgs bundles and K3 surfaces.

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BibTeXRIS

Sebastian Schlegel Mejia. 2023-10-04. BPS cohomology for rank 2 degree 0 Higgs bundles (and more). https://doi.org/10.1016/j.jalgebra.2023.08.037

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