{
  "id": "1906.11309",
  "version": "v1",
  "published": "2019-06-26T19:36:53.000Z",
  "updated": "2019-06-26T19:36:53.000Z",
  "title": "Degree of irrationality of a very general abelian variety",
  "authors": [
    "Elisabetta Colombo",
    "Olivier Martin",
    "Juan Carlos Naranjo",
    "Gian Pietro Pirola"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Consider a very general abelian variety $A$ of dimension at least $3$ and an integer $0<d\\leq \\dim A$. We show that if the map $A^k\\to CH_0(A)$ has a $d$-dimensional fiber then $k\\geq d+(\\dim A+1)/2$. This extends results of the second-named author which covered the cases $d=1,2$. As a geometric application, we obtain that any dominant rational map from a very general abelian $g$-fold to $\\mathbb{P}^g$ has degree at least $(3\\dim A+1)/2$ for $g\\geq 3$. This improves results of Alzati and the last-named author in the case of a very general abelian variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-26T19:36:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05",
      "14C15"
    ],
    "keywords": [
      "general abelian variety",
      "irrationality",
      "dominant rational map",
      "dimensional fiber",
      "geometric application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}