{
  "id": "math/0211251",
  "version": "v5",
  "published": "2002-11-16T15:02:07.000Z",
  "updated": "2003-05-16T06:10:35.000Z",
  "title": "Canonical stability of 3-folds of general type with $p_g\\geq 3$",
  "authors": [
    "Meng Chen"
  ],
  "comment": "Latex 14 pages, the final version, to appear in International Journal of Mathematics",
  "journal": "International Journal of Math. 14(2003), 515-528",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the canonical stability of a smooth projective 3-fold $V$ of general type. We prove that (1) $|5K_V|$ gives a birational map onto its image provided the geometric genus $p_g\\geq 4$; (2) $|6K_V|$ gives a birational map provided $p_g=3$. Known examples show that both are optimal. This fact can be viewed as parallel to surface case, though people know very little on 3-folds of general type with $p_g\\leq 1$.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2003-05-16T06:10:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general type",
      "canonical stability",
      "birational map",
      "surface case",
      "geometric genus"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11251C"
    }
  }
}