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Mixed Hodge structures of configuration spaces
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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.
Forward citations
Cited by 2 Pith papers
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Motivic quasimap wall-crossing for Grassmannians
An explicit Q-algebra automorphism of symmetric functions, given by q-deformations of power sums, converts the S_n-equivariant Euler characteristics of stable map moduli spaces to those of ε-stable quasimap moduli spa...
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Universal compactified Jacobians: cohomological invariance and boundary combinatorics
Cohomology of fine compactified universal Jacobians is independent of degree and Pagani–Tommasi stability, proved by equivariant bijections of multidegree strata.
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