{
  "id": "1210.2670",
  "version": "v1",
  "published": "2012-10-09T17:22:53.000Z",
  "updated": "2012-10-09T17:22:53.000Z",
  "title": "Lectures on birational geometry",
  "authors": [
    "Caucher Birkar"
  ],
  "comment": "85 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Lecture notes of a course on birational geometry (taught at College de France, Winter 2011, with the support of Fondation Sciences Math\\'ematiques de Paris). Topics covered: introduction into the subject, contractions and extremal rays, pairs and singularities, Kodaira dimension, minimal model program, cone and contraction, vanishing, base point freeness, flips and local finite generation, pl flips and extension theorems, existence of minimal models and Mori fibre spaces, global finite generation, etc.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-09T17:22:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birational geometry",
      "local finite generation",
      "base point freeness",
      "mori fibre spaces",
      "minimal model program"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 85,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.2670B"
    }
  }
}