{
  "id": "math/9906130",
  "version": "v1",
  "published": "1999-06-18T19:02:38.000Z",
  "updated": "1999-06-18T19:02:38.000Z",
  "title": "Resolutions of Ideals of Uniform Fat Point Subschemes of P^2",
  "authors": [
    "Brian Harbourne",
    "Sandeep Holay",
    "Stephanie Fitchett"
  ],
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Let I be the ideal corresponding to a set of general points $p_1,...,p_n \\in P^2$. There recently has been progress in showing that a naive lower bound for the Hilbert functions of symbolic powers $I^{(m)}$ is in fact attained when n>9. Here, for m sufficiently large, the minimal free graded resolution of $I^{(m)}$ is determined when n>9 is an even square, assuming only that this lower bound on the Hilbert function is attained. Under ostensibly stronger conditions (that are nonetheless expected always to hold), a similar result is shown to hold for odd squares, and for infinitely many m for each nonsquare n bigger than 9. All results hold for an arbitrary algebraically closed field k.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-06-18T19:02:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13P10",
      "14C99"
    ],
    "keywords": [
      "uniform fat point subschemes",
      "hilbert function",
      "minimal free graded resolution",
      "naive lower bound",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6130H"
    }
  }
}