{
  "id": "0804.4062",
  "version": "v1",
  "published": "2008-04-25T11:17:33.000Z",
  "updated": "2008-04-25T11:17:33.000Z",
  "title": "On the exceptional locus of the birational projections of normal surface singularity into a plane",
  "authors": [
    "Jesus Fernandez-Sanchez"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Given a normal surface singularity $(X, Q)$ and a birational morphism to a non- singular surface $\\pi : X \\to S$, we investigate the local geometry of the exceptional divisor $L$ of $\\pi$. We prove that the dimension of the tangent space to $L$ at $Q$ equals the number of exceptional components meeting at $Q$. Consequences relative to the existence of such birational projections contracting a prescribed number of irreducible curves are deduced. A new characterization of minimal singularities is obtained in these terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-25T11:17:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "14E05",
      "14J17"
    ],
    "keywords": [
      "normal surface singularity",
      "birational projections",
      "exceptional locus",
      "birational morphism",
      "minimal singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.4062F"
    }
  }
}