{
  "id": "0706.1794",
  "version": "v1",
  "published": "2007-06-13T14:16:48.000Z",
  "updated": "2007-06-13T14:16:48.000Z",
  "title": "Birational geometry",
  "authors": [
    "Caucher Birkar"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "This article contains the notes of a graduate course on birational geometry focusing on the minimal model program. Topics covered include singularities, vanishing, nonvanishing, cone and contraction, base point freeness, finite generation, flips, termination, minimal models and Mori fibre spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-13T14:16:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal model program",
      "base point freeness",
      "mori fibre spaces",
      "graduate course",
      "finite generation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.1794B"
    }
  }
}