{
  "id": "1309.6010",
  "version": "v2",
  "published": "2013-09-24T00:06:46.000Z",
  "updated": "2015-08-19T10:16:18.000Z",
  "title": "A birationality result for character varieties",
  "authors": [
    "Ben Klaff",
    "Stephan Tillmann"
  ],
  "comment": "8 pages; minor corrections in light of referee's comments; to appear in Mathematical Research Letters",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let M be an orientable, cusped hyperbolic 3-manifold of finite volume. We show that the restriction map from a Dehn surgery component in the PSL(2,C)-character variety of M to the character variety of the boundary of M is a birational isomorphism onto its image. This generalises a result by Nathan Dunfield. A key step in our proof is the exactness of Craig Hodgson's volume differential on the eigenvalue variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-24T00:06:46.000Z",
      "comment": "8 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-19T10:16:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "character variety",
      "birationality result",
      "craig hodgsons volume differential",
      "dehn surgery component",
      "restriction map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6010K"
    }
  }
}