Perverse sheaves on symmetric products of the plane

2022/08/30 by Tom Braden, Carl Mautner, Braden, Tom +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2208.14351

openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any field k, we give an algebraic description of the category Perv_\mathscrS(Sⁿ (ℂ²),k) of perverse sheaves on the n-fold symmetric product of the plane Sⁿ(ℂ²) constructible with respect to its natural stratification and with coefficients in k. In particular, we show that it is equivalent to the category of modules over a new algebra that is closely related to the Schur algebra. As part of our description we obtain an analogue of modular Springer theory for the Hilbert scheme Hilbⁿ(ℂ²) of n points in the plane with its Hilbert-Chow morphism.

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