{
  "id": "2007.11229",
  "version": "v1",
  "published": "2020-07-22T06:44:38.000Z",
  "updated": "2020-07-22T06:44:38.000Z",
  "title": "Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5",
  "authors": [
    "Cinzia Casagrande",
    "Eleonora A. Romano"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a smooth, complex Fano 4-fold, and rho(X) its Picard number. If X contains a prime divisor D with rho(X)-rho(D)>2, then either X is a product of del Pezzo surfaces, or rho(X)=5 or 6. In this setting, we completely classify the case where rho(X)=5; there are 6 families, among which one is new. We also deduce the classification of Fano 4-folds with rho(X)>4 with an elementary divisorial contraction sending a divisor to a curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-22T06:44:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "picard number",
      "lefschetz defect",
      "classification",
      "del pezzo surfaces",
      "complex fano"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}