{
  "id": "math/0110012",
  "version": "v3",
  "published": "2001-10-01T12:03:05.000Z",
  "updated": "2003-09-16T09:46:58.000Z",
  "title": "Inequalities of Noether type for 3-folds of general type",
  "authors": [
    "Meng Chen"
  ],
  "comment": "25 pages, the final version, to appear in \"Journal of the Mathematical Society of Japan\"",
  "categories": [
    "math.AG"
  ],
  "abstract": "If $X$ is a smooth complex projective 3-fold with ample canonical divisor $K$, then the inequality $K^3\\ge {2/3}(2p_g-7)$ holds, where $p_g$ denotes the geometric genus. This inequality is nearly sharp. We also give similar, but more complicated, inequalities for general minimal 3-folds of general type. (A noether type of inequality lies, by all means, on the other side of the Miyaoka-Yau inequality from the geographical point of view.)",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-09-16T09:46:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05"
    ],
    "keywords": [
      "general type",
      "noether type",
      "ample canonical divisor",
      "geometric genus",
      "general minimal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10012C"
    }
  }
}