{
  "id": "math/0502240",
  "version": "v2",
  "published": "2005-02-11T15:19:57.000Z",
  "updated": "2006-08-09T14:25:17.000Z",
  "title": "Syzygies, multigraded regularity and toric varieties",
  "authors": [
    "Milena Hering",
    "Hal Schenck",
    "Gregory G. Smith"
  ],
  "comment": "improved exposition and corrected typos",
  "journal": "Compositio Mathematica 142 (2006) 1499-1506",
  "doi": "10.1112/S0010437X0600251X",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Using multigraded Castelnuovo-Mumford regularity, we study the equations defining a projective embedding of a variety X. Given globally generated line bundles B_1, ..., B_k on X and integers m_1, ..., m_k, consider the line bundle L := B_1^m_1 \\otimes ... \\otimes B_k^m_k. We give conditions on the m_i which guarantee that the ideal of X in P(H^0(X,L)) is generated by quadrics and the first p syzygies are linear. This yields new results on the syzygies of toric varieties and the normality of polytopes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-08-09T14:25:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "13D02",
      "14C20",
      "52B20"
    ],
    "keywords": [
      "toric varieties",
      "multigraded regularity",
      "multigraded castelnuovo-mumford regularity",
      "globally generated line bundles",
      "conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2240H"
    }
  }
}