{
  "id": "math/0309399",
  "version": "v1",
  "published": "2003-09-24T12:06:56.000Z",
  "updated": "2003-09-24T12:06:56.000Z",
  "title": "Higher secant varieties of Segre-Veronese varieties",
  "authors": [
    "M. V. Catalisano",
    "A. V. Geramita",
    "A. Gimigliano"
  ],
  "comment": "12 pages, plain TEX",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the dimension of the higher secant varieties $X^s$ of ${\\Bbb X} = {\\Bbb P}^{n_1}\\times ...\\times {\\Bbb P}^{n_t}$ embedded the morphism given by ${\\cal O}_{\\Bbb X}({a_1,...,a_t})$. We call it a {\\it Segre-Veronese variety} and the embedding a {\\it Segre-Veronese embedding}. In several cases (e.g. for 3 factors {\\Bbb P}^{1}, or when $s$ is small) we show that $X^s$ has the expected dimension except for a few cases. A list of examples of defective $X^s$'s is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-24T12:06:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N15",
      "15A69"
    ],
    "keywords": [
      "higher secant varieties",
      "segre-veronese variety",
      "expected dimension"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9399C"
    }
  }
}