{
  "id": "1412.7023",
  "version": "v1",
  "published": "2014-12-22T15:16:30.000Z",
  "updated": "2014-12-22T15:16:30.000Z",
  "title": "On Gauss maps in positive characteristic in view of images, fibers, and field extensions",
  "authors": [
    "Katsuhisa Furukawa",
    "Atsushi Ito"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "The Gauss map of a projective variety $X \\subset \\mathbb{P}^N$ is a rational map from $X$ to a Grassmann variety. In positive characteristic, we show the following results. (1) For given projective varieties $F$ and $Y$, we construct a projective variety $X$ whose Gauss map has $F$ as its general fiber and has $Y$ as its image. More generally, we give such construction for families of varieties over $Y$ instead of fixed $F$. (2) At least in the case when the characteristic is not equal to $2$, any inseparable field extension appears as the extension induced from the Gauss map of some $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-22T15:16:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N05"
    ],
    "keywords": [
      "gauss map",
      "positive characteristic",
      "projective variety",
      "inseparable field extension appears",
      "general fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.7023F"
    }
  }
}