{
  "id": "1207.0208",
  "version": "v3",
  "published": "2012-07-01T13:51:13.000Z",
  "updated": "2014-07-11T17:07:09.000Z",
  "title": "Polyhedral divisors and torus actions of complexity one over arbitrary fields",
  "authors": [
    "Kevin Langlois"
  ],
  "comment": "We changed the title by a more attractive. No results affected. Final version",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that the presentation of affine $\\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra associated to a polyhedral divisor changes when we extend the scalars. As another application, we provide a combinatorial description of affine $\\mathbf{G}$-varieties of complexity one over a field, where $\\mathbf{G}$ is a (not-nescessary split) torus, by using elementary facts on Galois descent. This class of affine $\\mathbf{G}$-varieties is described via a new combinatorial object, which we call (Galois) invariant polyhedral divisor.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-11T17:07:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary field",
      "torus actions",
      "complexity",
      "polyhedral divisors holds",
      "invariant polyhedral divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0208L"
    }
  }
}