{
  "id": "1906.06160",
  "version": "v1",
  "published": "2019-06-12T22:07:39.000Z",
  "updated": "2019-06-12T22:07:39.000Z",
  "title": "Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case",
  "authors": [
    "Zbigniew Jelonek",
    "Michał Lasoń"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1501.00223",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $f:\\mathbb{K}^n\\rightarrow\\mathbb{K}^m$ be a generically finite polynomial map of degree $d$ between affine spaces. In arXiv:1411.5011 we proved that if $\\mathbb{K}$ is the field of complex or real numbers, then the set $S_f$ of points at which $f$ is not proper, is covered by polynomial curves of degree at most $d-1$. In this paper we generalize this result to positive characteristic. We provide a geometric proof of an upper bound by $d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-12T22:07:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R25",
      "14R99"
    ],
    "keywords": [
      "positive characteristic case",
      "non-properness set",
      "quantitative properties",
      "generically finite polynomial map",
      "geometric proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}