{
  "id": "2411.14645",
  "version": "v1",
  "published": "2024-11-22T00:30:38.000Z",
  "updated": "2024-11-22T00:30:38.000Z",
  "title": "Codimension two torus actions on the affine space",
  "authors": [
    "Alvaro Liendo",
    "Charlie Petitjean"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we classify smooth, contractible affine varieties equipped with faithful torus actions of complexity two, having a unique fixed point and a two-dimensional algebraic quotient isomorphic to a toric blow-up of a toric surface. These varieties are of particular interest as they represent the simplest candidates for potential counterexamples to the linearization conjecture in affine geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-22T00:30:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14R05",
      "14R10",
      "14R20"
    ],
    "keywords": [
      "affine space",
      "two-dimensional algebraic quotient isomorphic",
      "codimension",
      "faithful torus actions",
      "unique fixed point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}