{
  "id": "1210.1795",
  "version": "v4",
  "published": "2012-10-05T15:48:20.000Z",
  "updated": "2012-12-24T09:15:45.000Z",
  "title": "Syzygies of Jacobian ideals and defects of linear systems",
  "authors": [
    "Alexandru Dimca"
  ],
  "comment": "version 4: the discussion of the case when the singular locus is a complete intersection is added. The a-invariant and the Castelnuovo-Mumford regularity of the Milnor algebra are also explored",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Our main result describes the relation between the syzygies involving the first order partial derivatives $f_0,...,f_n$ of a homogeneous polynomial $f\\in \\C[x_0,...x_n]$ and the defect of the linear systems vanishing on the singular locus subscheme $\\Sigma_f=V(f_0,...,f_n)$ of the hypersurface $D:f=0$ in the complex projective space $\\PP^n$, when $D$ has only isolated singularities.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-12-24T09:15:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "13D40",
      "14C20",
      "13D02"
    ],
    "keywords": [
      "jacobian ideals",
      "first order partial derivatives",
      "singular locus subscheme",
      "complex projective space",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.1795D"
    }
  }
}