{
  "id": "math/0111039",
  "version": "v1",
  "published": "2001-11-04T18:33:15.000Z",
  "updated": "2001-11-04T18:33:15.000Z",
  "title": "Lines on algebraic varieties",
  "authors": [
    "J. M. Landsberg"
  ],
  "comment": "3 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "A variety $X$ is covered by lines if there exist a finite number of lines contained in $X$ passing through each general point. I prove two theorems. Theorem 1:Let $X^n\\subset P^M$ be a variety covered by lines. Then there are at most $n!$ lines passing through a general point of $X$. Theorem 2:Let $X^n\\subsetP^{n+1}$ be a hypersurface and let $x\\in X$ be a general point. If the set of lines having contact to order $k$ with $X$ at $x$ is of dimension greater than expected, then the lines having contact to order $k$ are actually contained in $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-11-04T18:33:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic varieties",
      "general point",
      "finite number",
      "dimension greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....11039L"
    }
  }
}