{
  "id": "math/0107041",
  "version": "v1",
  "published": "2001-07-05T16:41:28.000Z",
  "updated": "2001-07-05T16:41:28.000Z",
  "title": "Compactification of configuration spaces via Hilbert schemes",
  "authors": [
    "Laurent Evain"
  ],
  "comment": "34 pages, in french",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let F(X,n):= X^n-\\Delta be the complementary of the union \\Delta of the diagonals of X^n and let U be a quotient of F(X,n) (possibly trivial) by a subgroup of the symmetric group S_n. We construct compactifications of U in products of Hilbert schemes. Our approach generalizes and unifies classical constructions by Schubert-Semple, Le Barz-Keel, Kleiman and Cheah. An extensive study is done in the case n<4. This includes in particular a complete classification and a description of the quotients by the natural actions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-07-05T16:41:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C05"
    ],
    "keywords": [
      "hilbert schemes",
      "configuration spaces",
      "natural actions",
      "construct compactifications",
      "approach generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "fr",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7041E"
    }
  }
}