{
  "id": "math/0503498",
  "version": "v5",
  "published": "2005-03-23T16:50:33.000Z",
  "updated": "2006-12-07T00:24:37.000Z",
  "title": "Syzygies of curves and the effective cone of \\bar{M}_g",
  "authors": [
    "Gavril Farkas"
  ],
  "comment": "34 pages; Typos corrected. Version published in Duke Math. J",
  "journal": "Duke Math. J. 135 (2006), 53-99.",
  "categories": [
    "math.AG"
  ],
  "abstract": "We describe a systematic way of constructing effective divisors on the moduli space of stable curves of genus g having exceptionally small slope. We prove that any divisor on \\bar{M}_g consisting of curves failing a certain Green-Lazarsfeld syzygy type condition, provides a counterexample to the Harris-Morrison Slope Conjecture. These divisors generalize our original isolated counterexample to the Slope Conjecture which was the divisor on M_{10} of curves lying on K3 surfaces. We also introduce a new stratification of M_g, somewhat similar to the classical stratification given by gonality, but where the analogue of hyperelliptic curves are sections of K3 surfaces. Finally, we prove that various moduli spaces M_{g,n} with g<23 are of general type.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2006-12-07T00:24:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10"
    ],
    "keywords": [
      "effective cone",
      "moduli space",
      "k3 surfaces",
      "green-lazarsfeld syzygy type condition",
      "harris-morrison slope conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3498F"
    }
  }
}