{
  "id": "2006.14520",
  "version": "v1",
  "published": "2020-06-25T16:12:09.000Z",
  "updated": "2020-06-25T16:12:09.000Z",
  "title": "On Hodge polynomials of Singular Character Varieties",
  "authors": [
    "Carlos Florentino",
    "Azizeh Nozad",
    "Jaime Silva",
    "Alfonso Zamora"
  ],
  "comment": "To appear in the Proceedings of the Special Session on Complex Geometry of the ISAAC conference, Aveiro, Portugal (2019)",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Let $\\mathcal{X}_{\\Gamma}G:=\\mathrm{Hom}(\\Gamma,G)/\\!/G$ be the $G$-character variety of $\\Gamma$, where $G$ is a complex reductive group and $\\Gamma$ a finitely presented group. We introduce new techniques for computing Hodge-Deligne and Serre polynomials of $\\mathcal{X}_{\\Gamma}G$, and present some applications, focusing on the cases when $\\Gamma$ is a free or free abelian group. Detailed constructions and proofs of the main results will appear elsewhere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-25T16:12:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "32S35",
      "14D20"
    ],
    "keywords": [
      "character variety",
      "singular character varieties",
      "hodge polynomials",
      "free abelian group",
      "serre polynomials"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}