{
  "id": "1404.1757",
  "version": "v1",
  "published": "2014-04-07T12:05:41.000Z",
  "updated": "2014-04-07T12:05:41.000Z",
  "title": "Linear normality of general linear sections and some graded Betti numbers of 3-regular projective schemes",
  "authors": [
    "Jeaman Ahn",
    "Kangjin Han"
  ],
  "comment": "19pages, comments welcomed",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "In this paper we study graded Betti numbers of any nondegenerate 3-regular algebraic set $X$ in a projective space $\\mathbb P^{n}$. More concretely, via Generic initial ideals (Gins) method we mainly consider `tailing' Betti numbers, whose homological index is not less than $\\mathrm{codim}(X,\\mathbb P^{n})$. For this purpose, we first introduce a key definition `$\\mathrm{ND(1)}$ property', which provides a suitable ground where one can generalize the concepts such as `being nondegenerate' or `of minimal degree' from the case of varieties to the case of more general closed subschemes and give a clear interpretation on the tailing Betti numbers. Next, we recall basic notions and facts on Gins theory and we analyze the generation structure of the reverse lexicographic (rlex) Gins of 3-regular $\\mathrm{ND(1)}$ subschemes. As a result, we present exact formulae for these tailing Betti numbers, which connect them with linear normality of general linear sections of $X\\cap \\Lambda$ with a linear subspace $\\Lambda$ of dimension at least $\\mathrm{codim}(X,\\mathbb P^{n})$. Finally, we consider some applications and related examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-07T12:05:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N05",
      "13D02"
    ],
    "keywords": [
      "general linear sections",
      "linear normality",
      "projective schemes",
      "tailing betti numbers",
      "recall basic notions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.1757A"
    }
  }
}