Mixed Hodge structures of configuration spaces

1995/10/31 by Ezra Getzler, Getzler, Ezra · 9 citations
Mathematics · #14F40 (Primary) 20C30 (Secondary) #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.alg-geom/9510018

openalex publication_date 1995/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The symmetric group S_n acts freely on the configuration space of n distinct points in a quasi-projective variety. In this paper, we study the induced action of the symmetric group S_n on the de Rham cohomology of this space, using mixed Hodge theory, combined with methods from the theory of symmetric functions. (We prove a motivic version of this as well.) As an application of our results, we calculate the S_n-equivariant Hodge polynomial of the Fulton-MacPherson compactification X[n] of the configuration space.

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