{
  "id": "1507.03824",
  "version": "v1",
  "published": "2015-07-14T12:38:06.000Z",
  "updated": "2015-07-14T12:38:06.000Z",
  "title": "On K3 surface quotients of K3 or Abelian surfaces",
  "authors": [
    "Alice Garbagnati"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "The aim of this paper is to prove that a K3 surface is the minimal model of the quotient of an Abelian surface by a group $G$ (respectively of a K3 surface by an Abelian group $G$) if and only if a certain lattice is primitively embedded in its N\\'eron--Severi group. This allows one to describe the coarse moduli space of the K3 surfaces which are (rationally) $G$-covered by Abelian or K3 surfaces (in the latter case $G$ is an Abelian group). If either $G$ has order 2 or $G$ is cyclic and acts on an Abelian surface, this result was already known, so we extend it to the other cases. Moreover, we prove that a K3 surface $X_G$ is the minimal model of the quotient of an Abelian surface by a group $G$ if and only if a certain configuration of rational curves is present on $X_G$. Again this result was known only in some special cases, in particular if $G$ has order 2 or 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-14T12:38:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "14J50",
      "14J10"
    ],
    "keywords": [
      "abelian surface",
      "k3 surface quotients",
      "abelian group",
      "minimal model",
      "coarse moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}