{
  "id": "2002.01906",
  "version": "v1",
  "published": "2020-02-05T18:16:12.000Z",
  "updated": "2020-02-05T18:16:12.000Z",
  "title": "Bounding tangencies of sections on elliptic surfaces",
  "authors": [
    "Douglas Ulmer",
    "Giancarlo Urzúa"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Given an elliptic surface $\\mathcal{E}\\to\\mathcal{C}$ over a field $k$ of characteristic zero equipped with zero section $O$ and another section $P$ of infinite order, we give a simple and explicit upper bound on the number of points where $O$ is tangent to a multiple of $P$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-05T18:16:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J27",
      "11B39"
    ],
    "keywords": [
      "elliptic surface",
      "bounding tangencies",
      "explicit upper bound",
      "zero section",
      "infinite order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}