Mixed Hodge structures of configuration spaces
Abstract
The symmetric group Sn 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 Sn 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 Sn-equivariant Hodge polynomial of the Fulton-MacPherson compactification X[n] of the configuration space.
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