{
  "id": "1911.09457",
  "version": "v1",
  "published": "2019-11-21T13:19:03.000Z",
  "updated": "2019-11-21T13:19:03.000Z",
  "title": "Secant varieties of non-expected dimension on algebraic curves",
  "authors": [
    "Mara Ungureanu"
  ],
  "comment": "17 pages. Comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "The aim of this paper is to exhibit some surprising examples of secant varieties on a general curve that are empty despite their expected dimension being non-negative. We do so by reformulating the problem in terms of refined de Jonqui\\`eres divisors, that is divisors with prescribed multiplicities and dimensions on the curve. Our examples occur via the study of the dimension theory of refined de Jonqui\\`eres divisors in some relevant cases and degeneration arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-21T13:19:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "secant varieties",
      "algebraic curves",
      "non-expected dimension",
      "general curve",
      "empty despite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}