Mirror symmetry for parabolic Higgs bundles via $p$-adic integration

Abstract

Applying the technique of $p$-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups ${\text{SL}}_n$ and ${\text{PGL}}_n$, building on previous work of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the $E$-polynomial of the smooth moduli space of parabolic ${\text{GL}}_n$-Higgs bundles is independent of the degree of the underlying vector bundles.

33 pages. Refereed version

Cited by in corpus (1)

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