{
  "id": "1110.3028",
  "version": "v2",
  "published": "2011-10-13T18:54:05.000Z",
  "updated": "2011-10-18T10:47:54.000Z",
  "title": "Acyclic curves and group actions on affine toric surfaces",
  "authors": [
    "I. Arzhantsev",
    "M. Zaidenberg"
  ],
  "comment": "29p., added reference",
  "journal": "In: Affine Algebraic Geometry, World Scientific Publ., 2013, 1-41",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that every irreducible, simply connected curve on a toric affine surface X over the field of complex numbers is an orbit closure of a multiplicative group action on X. It follows that up to the action of the automorphism group Aut(X) there are only finitely many non-equivalent embeddings of the affine line in X. A similar description is given for simply connected curves in the quotients of the affine plane by small finite linear groups. We provide also an analog of the Jung-van der Kulk theorem for affine toric surfaces, and apply this to study actions of algebraic groups on such surfaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-18T10:47:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H45",
      "14M25",
      "14H50",
      "14R20"
    ],
    "keywords": [
      "affine toric surfaces",
      "acyclic curves",
      "small finite linear groups",
      "jung-van der kulk theorem",
      "simply connected curve"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3028A"
    }
  }
}