{
  "id": "0810.4571",
  "version": "v1",
  "published": "2008-10-25T01:25:31.000Z",
  "updated": "2008-10-25T01:25:31.000Z",
  "title": "Smoothness and jet schemes",
  "authors": [
    "Shihoko Ishii"
  ],
  "comment": "12 pages, to appear in Advanced Studies in Pure Math",
  "categories": [
    "math.AG"
  ],
  "abstract": "This paper shows some criteria for a scheme of finite type over an algebraically closed field to be non-singular in terms of jet schemes. For the base field of characteristic zero, the scheme is non-singular if and only if one of the truncation morphisms of its jet schemes is flat. For the positive characteristic case, we obtain a similar characterization under the reducedness condition on the scheme. We also obtain by a simple discussion that the scheme is non-singular if and only if one of its jet schemes is non-singular.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-25T01:25:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05"
    ],
    "keywords": [
      "jet schemes",
      "smoothness",
      "non-singular",
      "simple discussion",
      "base field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4571I"
    }
  }
}