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Resumo(s)
Let F be a finite group and X be a complex quasi-projective F-variety. For r is an element of N, we consider the mixed Hodge-Deligne polynomials of quotients X-r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple mixed Hodge structures (MHSs). A particularly interesting case is when X is the maximal torus of an affine reductive group G, and F is its Weyl group. As an application, we obtain explicit formulas for the Hodge-Deligne and E-polynomials of (the distinguished component of) G-character varieties of free abelian groups. In the cases G = GL(n, C) and SL(n, C), we get even more concrete expressions for these polynomials, using the combinatorics of partitions.
Descrição
Palavras-chave
Free abelian group Character variety Mixed Hodge structures Hodge-Deligne polynomials Equivariant E-polynomials Finite quotients
Contexto Educativo
Citação
FLORENTINO, Carlos; SILVA, Jaime – Hodge-deligne polynomials of character varieties of free abelian groups. Open Mathematics. ISSN 2391-5455. Vol. 19, N.º 1 (2021), pp. 338-362.
Editora
DE GRUYTER POLAND