{
  "id": "2308.07904",
  "version": "v1",
  "published": "2023-08-15T17:43:54.000Z",
  "updated": "2023-08-15T17:43:54.000Z",
  "title": "Automorphisms of quartic del Pezzo surfaces in characteristic zero",
  "authors": [
    "Jonathan M. Smith"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "For each field $k$ of characteristic zero, we classify which groups act by automorphisms on a quartic del Pezzo surface over $k$. We also determine which groups act on $k$-rational, stably $k$-rational, or $k$-unirational quartic del Pezzo surfaces. For each group $G$ that is realized over $k$, we exhibit explicit equations for a quartic del Pezzo surface $X$ in $\\mathbb{P}^4_k$ such that $G$ acts by automorphisms on $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-15T17:43:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J50",
      "14J45",
      "14E08"
    ],
    "keywords": [
      "characteristic zero",
      "automorphisms",
      "unirational quartic del pezzo surfaces",
      "groups act",
      "explicit equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}