{
  "id": "2102.01207",
  "version": "v1",
  "published": "2021-02-01T22:08:18.000Z",
  "updated": "2021-02-01T22:08:18.000Z",
  "title": "Order 3 symplectic automorphisms on K3 surfaces",
  "authors": [
    "Alice Garbagnati",
    "Yulieth Prieto Montañez"
  ],
  "comment": "31 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "The aim of this paper is to generalize results known for the symplectic involutions on K3 surfaces to the order 3 symplectic automorphisms on K3 surfaces. In particular, we will explicitly describe the action induced on the lattice $\\Lambda_{K3}$, isometric to the second cohomology group of a K3 surface, by a symplectic automorphism of order 3; we exhibit the maps $\\pi_*$ and $\\pi^*$ induced in cohomology by the rational quotient map $\\pi:X\\dashrightarrow Y$, where $X$ is a K3 surface admitting an order 3 symplectic automorphism $\\sigma$ and $Y$ is the minimal resolution of the quotient $X/\\sigma$; we deduce the relation between the N\\'eron--Severi group of $X$ and the one of $Y$. Applying these results we describe explicit geometric examples and generalize the Shioda--Inose structures, relating Abelian surfaces admitting order 3 endomorphisms with certain specific K3 surfaces admitting particular order 3 symplectic automorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-01T22:08:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "14J50"
    ],
    "keywords": [
      "symplectic automorphism",
      "explicit geometric examples",
      "rational quotient map",
      "relating abelian surfaces admitting order",
      "second cohomology group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}