{
  "id": "1004.2614",
  "version": "v1",
  "published": "2010-04-15T12:02:04.000Z",
  "updated": "2010-04-15T12:02:04.000Z",
  "title": "Higher secant varieties of $\\mathbb{P}^n \\times \\mathbb{P}^m$ embedded in bi-degree $(1,d)$",
  "authors": [
    "Alessandra Bernardi",
    "Enrico Carlini",
    "Maria Virginia Catalisano"
  ],
  "comment": "8 pages",
  "journal": "J. Pure Appl. Algebra. 215, (2011), pp. 2853-2858",
  "doi": "10.1016/j.jpaa.2011.04.005",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X^{(n,m)}_{(1,d)}$ denote the Segre-Veronese embedding of $\\mathbb{P}^n \\times \\mathbb{P}^m$ via the sections of the sheaf $\\mathcal{O}(1,d)$. We study the dimensions of higher secant varieties of $X^{(n,m)}_{(1,d)}$ and we prove that there is no defective $s^{th}$ secant variety, except possibly for $n$ values of $s$. Moreover when ${m+d \\choose d}$ is multiple of $(m+n+1)$, the $s^{th}$ secant variety of $X^{(n,m)}_{(1,d)}$ has the expected dimension for every $s$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-15T12:02:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher secant varieties",
      "secant variety",
      "segre-veronese",
      "expected dimension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.2614B"
    }
  }
}