{
  "id": "1108.4007",
  "version": "v1",
  "published": "2011-08-19T17:02:54.000Z",
  "updated": "2011-08-19T17:02:54.000Z",
  "title": "Minimal Free Resolutions of 0-Dimensional Schemes in P1 \\times P1",
  "authors": [
    "Paola Bonacini",
    "Lucia Marino"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a zero-dimensional scheme in P1 \\times P1. Then X has a minimal free resolution of length 2 if and only if X is ACM. In this paper we determine a class of reduced schemes whose resolutions, similarly to the ACM case, can be obtained by their Hilbert functions and depends only on their distributions of points in a grid of lines. Moreover, a minimal set of generators of the ideal of these schemes is given by curves split into the union of lines.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-19T17:02:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D02",
      "13D40",
      "13H10"
    ],
    "keywords": [
      "minimal free resolution",
      "acm case",
      "zero-dimensional scheme",
      "hilbert functions",
      "minimal set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4007B"
    }
  }
}