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Mixed Hodge structures of configuration spaces

Ezra Getzler
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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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Ezra Getzler. 1996-05-19. Mixed Hodge structures of configuration spaces. https://arxiv.org/abs/alg-geom/9510018

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