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

2018/10/12 by Junliang Shen, Zili Zhang, Shen, Junliang +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1810.05330

openalex publication_date 2018/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove de Cataldo-Hausel-Migliorini's P=W conjecture in arbitrary rank for parabolic Higgs bundles labeled by the affine Dynkin diagrams A₀, D₄, E₆, E₇, and E₈. 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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