{
  "id": "1409.0927",
  "version": "v1",
  "published": "2014-09-03T00:09:33.000Z",
  "updated": "2014-09-03T00:09:33.000Z",
  "title": "The Hurwitz space of covers of an elliptic curve $E$ and the Severi variety of curves in $E \\times \\mathbb{P}^1$",
  "authors": [
    "Gabriel Bujokas"
  ],
  "comment": "With 18 figures. Comments are very welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "We describe the hyperplane sections of the Severi variety of curves in $E \\times \\mathbb{P}^1$ in a similar fashion to Caporaso-Harris' seminal work. From this description we almost get a recursive formula for the Severi degrees (we get the terms, but not the coefficients). As an application, we determine the components of the Hurwitz space of simply branched covers of a genus one curve. In return, we use this characterization to describe the components of the Severi variety of curves in $E \\times \\mathbb{P}^1$, in a restricted range of degrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-03T00:09:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H52",
      "14H30",
      "14H10",
      "14N35"
    ],
    "keywords": [
      "severi variety",
      "hurwitz space",
      "elliptic curve",
      "components",
      "hyperplane sections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.0927B"
    }
  }
}