{
  "id": "math/0601189",
  "version": "v1",
  "published": "2006-01-09T19:40:58.000Z",
  "updated": "2006-01-09T19:40:58.000Z",
  "title": "Projective Normality Of Algebraic Curves And Its Application To Surfaces",
  "authors": [
    "Seonja Kim",
    "YoungRock Kim"
  ],
  "comment": "7 pages, 1figure",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $L$ be a very ample line bundle on a smooth curve $C$ of genus $g$ with $\\frac{3g+3}{2}<\\deg L\\le 2g-5$. Then $L$ is normally generated if $\\deg L>\\max\\{2g+2-4h^1(C,L), 2g-\\frac{g-1}{6}-2h^1(C,L)\\}$. Let $C$ be a triple covering of genus $p$ curve $C'$ with $C\\stackrel{\\phi}\\to C'$ and $D$ a divisor on $C'$ with $4p<\\deg D< \\frac{g-1}{6}-2p$. Then $K_C(-\\phi^*D)$ becomes a very ample line bundle which is normally generated. As an application, we characterize some smooth projective surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-09T19:40:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H45",
      "14H10",
      "14C20",
      "14J10",
      "14J27",
      "14J28"
    ],
    "keywords": [
      "algebraic curves",
      "projective normality",
      "ample line bundle",
      "application",
      "smooth curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1189K"
    }
  }
}