{
  "id": "1708.01029",
  "version": "v1",
  "published": "2017-08-03T07:23:16.000Z",
  "updated": "2017-08-03T07:23:16.000Z",
  "title": "Ranks on the boundaries of secant varieties",
  "authors": [
    "Edoardo Ballico"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "In many cases (e.g. for many Segre or Segre embeddings of multiprojective spaces) we prove that a hypersurface of the $b$-secant variety of $X\\subset \\mathbb {P}^r$ has $X$-rank $>b$. We prove it proving that the $X$-rank of a general point of the join of $b-2$ copies of $X$ and the tangential variety of $X$ is $>b$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-03T07:23:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N05",
      "15A69"
    ],
    "keywords": [
      "secant variety",
      "boundaries",
      "tangential variety",
      "segre embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}