{
  "id": "math/0305112",
  "version": "v3",
  "published": "2003-05-07T17:59:38.000Z",
  "updated": "2004-08-31T20:01:23.000Z",
  "title": "Effective divisors on \\bar{M}_g, curves on K3 surfaces and the Slope Conjecture",
  "authors": [
    "Gavril Farkas",
    "Mihnea Popa"
  ],
  "comment": "This version combines our earlier preprints \"Effective divisors on M_g and a counterexample to the Slope Conjecture\" and \"The geometry of the divisor of K3 sections\" into a single paper. To appear in the Journal of Algebraic Geometry",
  "categories": [
    "math.AG"
  ],
  "abstract": "We carry out a detailed intersection theoretic analysis of the Deligne-Mumford compactification of the divisor on M_{10} consisting of curves sitting on K3 surfaces. This divisor is not of classical Brill-Noether type, and is known to give a counterexample to the Slope Conjecture. The computation relies on the fact that this divisor has four different incarnations as a geometric subvariety of the moduli space of curves, one of them as a higher rank Brill-Noether divisor consisting of curves with an exceptional rank 2 vector bundle. As an application we describe the birational nature of the moduli space of n-pointed curves of genus 10, for all n. We also show that on M_{11} there are effective divisors of minimal slope and having large Iitaka dimension. This seems to contradict the belief that on M_g the classical Brill-Noether divisors are essentially the only ones of slope 6+12/(g+1).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-08-31T20:01:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10"
    ],
    "keywords": [
      "k3 surfaces",
      "slope conjecture",
      "effective divisors",
      "moduli space",
      "classical brill-noether"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......5112F"
    }
  }
}