{
  "id": "math/0401375",
  "version": "v1",
  "published": "2004-01-27T13:40:34.000Z",
  "updated": "2004-01-27T13:40:34.000Z",
  "title": "Caractères numériques",
  "authors": [
    "Mireille Martin-Deschamps"
  ],
  "comment": "25 pages latex",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "The postulation of Arithmetically Cohen-Macaulay (ACM) subschemes of the projective space ${\\mathbb P}^N_k$ is well-known in the case of codimension 2. There are many different ways of recording this numerical information : numerical character of Gruson/Peskine, $h$-vector, postulation character of Martin-Deschamps/Perrin... The first aim of this paper is to show the equivalence between these notions. The second, and most important aim, is to study the postulation of codimension 3 ACM subschemes of ${\\mathbb P}^N$. We use a result of Macaulay which describes all the Hilbert functions of the quotients of a polynomial ring. By iterating the number of variables, we obtain a new form of the growth of these functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-27T13:40:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M05",
      "14Q05",
      "13P99"
    ],
    "keywords": [
      "caractères numériques",
      "codimension",
      "first aim",
      "important aim",
      "acm subschemes"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1375M"
    }
  }
}