{
  "id": "math/0110083",
  "version": "v1",
  "published": "2001-10-08T12:23:29.000Z",
  "updated": "2001-10-08T12:23:29.000Z",
  "title": "Infinitesimal Extensions of P^1 and their Hilbert Schemes",
  "authors": [
    "Nikolaos Tziolas"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In order to calculate the multiplicity of an isolated rational curve C in a local complete intersection variety X, i.e. the length of the Hilbert scheme of X at [C], it is important to study infinitesimal neighborhoods of the curve in X. This is equivalent to infinitesimal extensions of P^1 by locally free sheaves. In this paper we study infinitesimal extensions of P^1, determine their structure and obtain upper and lower bounds for the length of the local rings of their Hilbert schemes at [P^].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-08T12:23:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C05"
    ],
    "keywords": [
      "hilbert scheme",
      "local complete intersection variety",
      "study infinitesimal neighborhoods",
      "study infinitesimal extensions",
      "isolated rational curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10083T"
    }
  }
}