Perverse filtrations, Hilbert schemes, and the P=W conjecture for parabolic Higgs bundles

Abstract

We prove de Cataldo-Hausel-Migliorini's P=W conjecture in arbitrary rank for parabolic Higgs bundles labeled by the affine Dynkin diagrams ${\tilde{A}}_0$, ${\tilde{D}}_4$, ${\tilde{E}}_6$, ${\tilde{E}}_7$, and ${\tilde{E}}_8$. Our proof relies on the study of the tautological classes on the Hilbert scheme of points on an elliptic surface with respect to the perverse filtration.

30 pages. Comments are welcome!