{
  "id": "1803.03138",
  "version": "v1",
  "published": "2018-03-08T14:58:00.000Z",
  "updated": "2018-03-08T14:58:00.000Z",
  "title": "Tropes, Torelli and theta characteristics",
  "authors": [
    "M. J. Fryers",
    "N. I. Shepherd-Barron"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Our main result is an effective version of the Torelli theorem in genus $3$ and any characteristic not $2$: the configuration of the odd theta characteristics of a curve $C$ of genus $3$ determines a del Pezzo surface $S$ of degree two and that $C$ is recovered as the normalization of a certain curve on $S$. This surface is not the one usually associated to $C$; we describe the distinction. We also give an explicit geometrical description of the quadratic twist (observed by Serre) that arises in the statement of the Torelli theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-08T14:58:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40"
    ],
    "keywords": [
      "torelli theorem",
      "odd theta characteristics",
      "del pezzo surface",
      "main result",
      "explicit geometrical description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}