{
  "id": "1809.05405",
  "version": "v1",
  "published": "2018-09-12T18:18:29.000Z",
  "updated": "2018-09-12T18:18:29.000Z",
  "title": "Smooth quotients of abelian surfaces by finite groups",
  "authors": [
    "Robert Auffarth",
    "Giancarlo Lucchini Arteche",
    "Pablo Quezada"
  ],
  "comment": "15 pages. Comments are welcome. arXiv admin note: text overlap with arXiv:1801.00028",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $A$ be an abelian surface and let $G$ be a finite group of automorphisms of $A$ fixing the origin. Assume that the analytic representation of $G$ is irreducible. We give a classification of the pairs $(A,G)$ such that the quotient $A/G$ is smooth. In particular, we prove that $A=E^2$ with $E$ an elliptic curve and that $A/G\\simeq\\mathbb P^2$ in all cases. Moreover, for fixed $E$, there are only finitely many pairs $(E^2,G)$ up to isomorphism. This completes the classification of smooth quotients of abelian varieties by finite groups started by the first two authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-12T18:18:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14K99"
    ],
    "keywords": [
      "finite group",
      "abelian surface",
      "smooth quotients",
      "classification",
      "abelian varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}