{
  "id": "0912.4342",
  "version": "v2",
  "published": "2009-12-22T09:02:56.000Z",
  "updated": "2011-06-29T14:32:01.000Z",
  "title": "On the dimensions of secant varieties of Segre-Veronese varieties",
  "authors": [
    "Hirotachi Abo",
    "Maria Chiara Brambilla"
  ],
  "comment": "Revised version. To appear in Annali di Matematica Pura e Applicata",
  "doi": "10.1007/s10231-011-0212-3",
  "categories": [
    "math.AG"
  ],
  "abstract": "This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the dimension of the secant variety in a high dimensional case to the computation of the dimensions of secant varieties in low dimensional cases. As an application of these inductive approaches, we will prove non-defectivity of secant varieties of certain two-factor Segre-Veronese varieties. We also use these methods to give a complete classification of defective s-th Segre-Veronese varieties for small s. In the final section, we propose a conjecture about defective two-factor Segre-Veronese varieties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-29T14:32:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J10",
      "14J26",
      "14Q10"
    ],
    "keywords": [
      "secant variety",
      "defective two-factor segre-veronese varieties",
      "high dimensional case",
      "higher secant varieties",
      "defective s-th segre-veronese varieties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.4342A"
    }
  }
}