{
  "id": "math/0502138",
  "version": "v2",
  "published": "2005-02-07T17:16:21.000Z",
  "updated": "2005-02-08T13:14:00.000Z",
  "title": "Characterizing Jacobians via flexes of the Kummer variety",
  "authors": [
    "E. Arbarello",
    "G. Marini",
    "I. Krichever"
  ],
  "comment": "14",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given an abelian variety $X$ and a point $a\\in X$ we denote by $<a>$ the closure of the subgroup of $X$ generated by $a$. Let $N=2^g-1$. We denote by $\\kappa: X\\to \\kappa(X)\\subset\\mathbb P^N$ the map from $X$ to its Kummer variety. We prove that an indecomposable abelian variety $X$ is the Jacobian of a curve if and only if there exists a point $a=2b\\in X\\setminus\\{0\\}$ such that $<a>$ is irreducible and $\\kappa(b)$ is a flex of $\\kappa(X)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-02-08T13:14:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kummer variety",
      "characterizing jacobians",
      "indecomposable abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2138A"
    }
  }
}