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arXiv · 1810.05330

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

Junliang Shen·Zili Zhang
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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.

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Junliang Shen, Zili Zhang. 2018-10-12. Perverse filtrations, Hilbert schemes, and the P=W conjecture for parabolic Higgs bundles. https://arxiv.org/abs/1810.05330

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