{
  "id": "2008.13427",
  "version": "v1",
  "published": "2020-08-31T08:36:29.000Z",
  "updated": "2020-08-31T08:36:29.000Z",
  "title": "Projective plane curves whose automorphism groups are simple and primitive",
  "authors": [
    "Yusuke Yoshida"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study complex projective plane curves with a given group of automorphisms. Let $G$ be a simple primitive subgroup of $PGL(3, \\mathbb{C})$, which is isomorphic to $A_{6}$, $A_{5}$ or $PSL(2, \\mathbb{F}_{7})$. We obtain a necessary and sufficient condition on $d$ for the existence of a nonsingular projective plane curve of degree $d$ invariant under $G$. We also study an analogous problem on integral curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-31T08:36:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H50",
      "14H37"
    ],
    "keywords": [
      "automorphism groups",
      "study complex projective plane curves",
      "nonsingular projective plane curve",
      "simple primitive subgroup",
      "integral curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}