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Mixed Hodge structures on character varieties of nilpotent groups

Algebraic Geometry 2025-02-06 v3 Representation Theory

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.

Keywords

Cite

@article{arxiv.2110.07060,
  title  = {Mixed Hodge structures on character varieties of nilpotent groups},
  author = {Carlos Florentino and Sean Lawton and Jaime Silva},
  journal= {arXiv preprint arXiv:2110.07060},
  year   = {2025}
}

Comments

23 pages; version 3 fixes typos and adds clarification, accepted for publication in Revista Matem\'atica Complutense