Mixed Hodge structures on character varieties of nilpotent groups

DOI10.1007/S13163-024-00490-9arXiv2110.07060MaRDI QIDQ6505210

Jaime Silva, Carlos Florentino, Sean Lawton

Abstract: Let R be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the representation variety R and on the character variety R//G. We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Mixed Hodge theory of singular varieties (complex-analytic aspects) (32S35) Character varieties (14M35)

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