Mixed Hodge structures of configuration spaces
alg-geom
2008-02-03 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.alg-geom/9510018,
title = {Mixed Hodge structures of configuration spaces},
author = {Ezra Getzler},
journal= {arXiv preprint arXiv:alg-geom/9510018},
year = {2008}
}
Comments
AmSLaTeX 1.v2, 18 pages, revised version