{
  "id": "1712.01587",
  "version": "v1",
  "published": "2017-12-05T11:54:33.000Z",
  "updated": "2017-12-05T11:54:33.000Z",
  "title": "$G$-birational rigidity of the projective plane",
  "authors": [
    "Dmitrijs Sakovics"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given a surface $S$ and a finite group $G$ of automorphisms of $S$, consider the birational maps $S\\dashrightarrow S'$ that commute with the action of $G$. This leads to the notion of a $G$-minimal variety. A natural question arises: for a fixed group $G$, is there a birational $G$-map between two different $G$-minimal surfaces? If no such map exists, the surface is said to be $G$-birationally rigid. This paper determines the $G$-rigidity of the projective plane for every finite subgroup $G\\subset\\mbox{PGL}_3\\left(\\mathbb{C}\\right)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-05T11:54:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E07",
      "14J45",
      "20C25"
    ],
    "keywords": [
      "projective plane",
      "birational rigidity",
      "natural question arises",
      "birational maps",
      "finite subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}