{
  "id": "1802.06661",
  "version": "v1",
  "published": "2018-02-19T15:02:45.000Z",
  "updated": "2018-02-19T15:02:45.000Z",
  "title": "On the Abel-Jacobi map of an elliptic surface and the topology of cubic-line arrangements",
  "authors": [
    "Shinzo Bannai",
    "Hiro-o Tokunaga"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "Let $S$ be an elliptic surface over a smooth curve $C$ with a section $O$. We denote its generic fiber by $E_S$. For a divisor $D$ on $S$, we canonically associate a $C(C)$-rational point $P_D$. In this note, we give a description of $P_D$ of $E_S$, when the rank of the group of $C(C)$-rational points is one. We apply our description to refine our result on a Zariski pair for a cubic-line arrangement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-19T15:02:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14F35",
      "14F45"
    ],
    "keywords": [
      "elliptic surface",
      "cubic-line arrangement",
      "abel-jacobi map",
      "rational point",
      "generic fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}