{
  "id": "0908.4500",
  "version": "v1",
  "published": "2009-08-31T10:49:12.000Z",
  "updated": "2009-08-31T10:49:12.000Z",
  "title": "Number of singular points of a genus $g$ curve with one point at infinity",
  "authors": [
    "Maciej Borodzik"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We bound the maximal number N of singular points of a plane algebraic curve C that has precisely one place at infinity with one branch in terms of its first Betti number $b_1(C)$. Asymptotically we prove that $N<\\sim{17/11}b_1(C)$ for large $b_1$. In particular, in the case of curves with one place at infinity, we confirm the Zaidenberg and Lin conjecture stating that $N\\le 2b_1+1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-31T10:49:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H50",
      "14H20",
      "32S50",
      "14E15"
    ],
    "keywords": [
      "singular points",
      "first betti number",
      "plane algebraic curve",
      "maximal number",
      "lin conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.4500B"
    }
  }
}