{
  "id": "2103.11159",
  "version": "v1",
  "published": "2021-03-20T11:32:34.000Z",
  "updated": "2021-03-20T11:32:34.000Z",
  "title": "Curves contracted by the Gauss map",
  "authors": [
    "Lei Song"
  ],
  "comment": "11 pages. Comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given a singular projective variety in some projective space, we characterize the smooth curves contracted by the Gauss map in terms of normal bundles. As a consequence, we show that if the variety is normal, then a contracted line always has local obstruction for the embedded deformation and each component of the Hilbert scheme where the line lies is non-reduced everywhere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-20T11:32:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gauss map",
      "smooth curves",
      "line lies",
      "normal bundles",
      "singular projective variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}