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Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces

2010/12/12 by Mark Andrea A. de Cataldo, de Cataldo, Mark Andrea A., Tamas Hausel +4
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1012.2583

19 pages

arxiv created 2010/12/12 · openalex publication_date 2010/12/12 · arxiv updated 2010/12/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bundle of an elliptic curve, exchanges the weight filtration on the first set of cohomology groups with the perverse Leray filtration associated with a natural fibration on the second set of cohomology groups. We discuss some associated hard Lefschetz phenomena.

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