Perversity equals weight for Painlevé spaces

2018/02/11 by Szilárd Szabó, Szabó, Szilárd · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1802.03798

openalex publication_date 2018/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide further evidence to the P=W conjecture of de Cataldo, Hausel and Migliorini, by checking it in the Painlevé cases. Namely, we compare the perverse Leray filtration induced by the Hitchin map on the cohomology spaces of the Dolbeault moduli space and the weight filtration on the cohomology spaces of the irregular character variety corresponding to each of the Painlevé I-VI systems. We find that the two filtrations agree. Along the way, we prove the Geometric P=W conjecture of Katzarkov, Noll, Pandit and Simpson in the Painlevé cases, and show that in these cases the Geometric P=W conjecture implies the P=W conjecture.

Cited by

• Bigraded Polynomials for the Cohomology of Wild Hitchin Systems
• Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence

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