{
  "id": "1806.05552",
  "version": "v1",
  "published": "2018-06-14T13:53:30.000Z",
  "updated": "2018-06-14T13:53:30.000Z",
  "title": "A criterion for existence of Néron models of jacobians",
  "authors": [
    "Giulio Orecchia"
  ],
  "comment": "35 pages. Comments are very welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "N\\'eron models of abelian varieties do not necessarily exist if the base $S$ has dimension higher than 1. We introduce a new condition, called toric additivity, on a family of smooth curves having nodal reduction over a normal crossing divisor $D\\subset S$. The condition is necessary and sufficient for existence of a N\\'eron model of the jacobian of the family; it depends only on the Betti numbers of the dual graphs of the fibres of the family, or on the toric ranks of the fibres of the jacobian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-14T13:53:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14D06"
    ],
    "keywords": [
      "néron models",
      "neron model",
      "dimension higher",
      "smooth curves",
      "nodal reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}