{
  "id": "0704.3994",
  "version": "v1",
  "published": "2007-04-30T18:43:14.000Z",
  "updated": "2007-04-30T18:43:14.000Z",
  "title": "Covers of Elliptic Curves and the Lower Bound for Slopes of Effective Divisors on $\\bar{\\mathcal M}_{g}$",
  "authors": [
    "Dawei Chen"
  ],
  "comment": "41 pages, 19 figures",
  "categories": [
    "math.AG",
    "math.CO",
    "math.GT"
  ],
  "abstract": "Consider genus $g$ curves that admit degree $d$ covers to elliptic curves only branched at one point with a fixed ramification type. The locus of such covers forms a one parameter family $Y$ that naturally maps into the moduli space of stable genus $g$ curves $\\bar{\\mathcal M}_{g}$. We study the geometry of $Y$, and produce a combinatorial method by which to investigate its slope, irreducible components, genus and orbifold points. As a by-product of our approach, we find some equalities from classical number theory. Moreover, a correspondence between our method and the viewpoint of square-tiled surfaces is established. We also use our results to study the lower bound for slopes of effective divisors on $\\bar{\\mathcal M}_{g}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-30T18:43:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14H30",
      "05A15",
      "05E15"
    ],
    "keywords": [
      "lower bound",
      "elliptic curves",
      "effective divisors",
      "admit degree",
      "classical number theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3994C"
    }
  }
}