{
  "id": "1107.4878",
  "version": "v2",
  "published": "2011-07-25T09:54:43.000Z",
  "updated": "2012-12-17T12:27:46.000Z",
  "title": "Minimal Model Program with scaling and adjunction theory",
  "authors": [
    "Marco Andreatta"
  ],
  "comment": "12 pages. Proposition 3.6 of the previous version was incomplete. Some proofs have been shortened. The paper will be published on International Journal of Mathematics",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let (X,L) be a quasi polarized pairs, i.e. X is a normal complex projective variety and L is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the adjoint bundles K_X + rL for high rational number r. For this we run a Minimal Model Program with scaling relative to the divisor K_X +rL. We give some applications, namely the classification up to birational equivalence of quasi polarized pairs with sectional genus 0,1 and of embedded projective varieties X < P^N with degree smaller than 2codim(X) +2.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-17T12:27:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30",
      "14J40",
      "14N30",
      "14N25"
    ],
    "keywords": [
      "minimal model program",
      "adjunction theory",
      "quasi polarized pairs",
      "birational equivalence",
      "normal complex projective variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.4878A"
    }
  }
}