Ansatz for (-1)^n-1∇ p_n

2018/06/14 by Soumya Dipta Banerjee, Banerjee, Soumya Dipta, Mahir Bilen Can +3
Mathematics · #05E05 #14C05 #14F99 #14L30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1806.05704

openalex publication_date 2018/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a special family of equivariant coherent sheaves on the Hilbert scheme on n-points in the affine plane. The equivariant Euler characteristic of these sheaves are closely related to the symmetic functions (-1)^n-1 ∇ p_n. We prove a higher cohomology vanishing result of these sheaves. It follows from the Bridgeland-King-Reid correspondence that there is an effective S_n module underlying the aforementioned family of symmetric functions.

Related

• Equivariant cohomology, symmetric functions and the Hilbert schemes of points on the total space of the invertible sheaf O(-2) over the projective line
• Nested Hilbert schemes and the nested q,t-Catalan series
• S_n-Equivariant Sheaves and Kozsul Cohomology
• Knot Homology and sheaves on the Hilbert scheme of points on the plane
• Cohomology of coherent sheaves on a proper scheme