{
  "id": "1704.04440",
  "version": "v1",
  "published": "2017-04-14T14:42:50.000Z",
  "updated": "2017-04-14T14:42:50.000Z",
  "title": "$\\mathbb{A}^2$ -Fibrations between affine spaces are trivial $\\mathbb{A}^2$-bundles",
  "authors": [
    "Adrien Dubouloz"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We give a criterion for a flat fibration with affine plane fibers over a smooth scheme defined over a field of characteristic zero to be a Zariski locally trivial $\\mathbb{A}^2$-bundle. An application is a positive answer to a version of the Dolgachev-Weisfeiler Conjecture for such fibrations: a flat fibration $\\mathbb{A}^m$ $\\rightarrow$ $\\mathbb{A}^n$ with all fibers isomorphic to $\\mathbb{A}^2$ is the trivial $\\mathbb{A}^2$-bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-14T14:42:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine spaces",
      "flat fibration",
      "affine plane fibers",
      "smooth scheme",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}