{
  "id": "1103.0483",
  "version": "v3",
  "published": "2011-03-02T16:41:54.000Z",
  "updated": "2012-02-23T16:16:05.000Z",
  "title": "Asymptotic syzygies of algebraic varieties",
  "authors": [
    "Lawrence Ein",
    "Robert Lazarsfeld"
  ],
  "comment": "Sections renumbered to conform to published version. To appear in Invent. Math",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "This paper studies the asymptotic behavior of the syzygies of a smooth projective variety X as the positivity of the embedding line bundle grows. We prove that as least as far as grading is concerned, the minimal resolution of the ideal of X has a surprisingly uniform asymptotic shape: roughly speaking, generators eventually appear in almost all degrees permitted by Castelnuovo-Mumford regularity. This suggests in particular that a widely-accepted intuition derived from the case of curves -- namely that syzygies become simpler as the degree of the embedding increases -- may have been misleading. For Veronese embeddings of projective space, we give an effective statement that in some cases is optimal, and conjecturally always is so. Finally, we propose a number of questions and open problems concerning asymptotic syzygies of higher-dimensional varieties.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-02-23T16:16:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic varieties",
      "open problems concerning asymptotic syzygies",
      "embedding line bundle grows",
      "surprisingly uniform asymptotic shape",
      "higher-dimensional varieties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00222-012-0384-5",
      "journal": "Inventiones Mathematicae",
      "year": 2012,
      "month": "Dec",
      "volume": 190,
      "number": 3,
      "pages": 603
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012InMat.190..603E"
    }
  }
}