{
  "id": "2003.01830",
  "version": "v1",
  "published": "2020-03-03T23:21:11.000Z",
  "updated": "2020-03-03T23:21:11.000Z",
  "title": "Models and Integral Differentials of Hyperelliptic Curves",
  "authors": [
    "Simone Muselli"
  ],
  "comment": "43 pages, Keywords: hyperelliptic curves, models of curves, integral differentials. Comments are welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $C:y^2=f(x)$ be a hyperelliptic curve of genus $g\\geq 2$, defined over a discretely valued complete field $K$, with ring of integers $O_K$. Under certain conditions on $C$, mild when residue characteristic is not $2$, we explicitly construct the minimal regular model with normal crossings $\\mathcal{C}/O_K$ of $C$. In the same setting we determine a basis of integral differentials of $C$, that is an $O_K$-basis for the global sections of the relative dualising sheaf $\\omega_{\\mathcal{C}/O_K}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-03T23:21:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "14H45"
    ],
    "keywords": [
      "hyperelliptic curve",
      "integral differentials",
      "minimal regular model",
      "global sections",
      "discretely valued complete field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}