Mixed Hodge structures of configuration spaces

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.

AmSLaTeX 1.v2, 18 pages, revised version

References in corpus (1)

• The motive of some moduli spaces of vector bundles over a curve

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