{
  "id": "2301.07055",
  "version": "v1",
  "published": "2023-01-17T18:16:37.000Z",
  "updated": "2023-01-17T18:16:37.000Z",
  "title": "On $G$-birational rigidity of del Pezzo surfaces",
  "authors": [
    "Egor Yasinsky"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $G$ be a finite group and $H\\subseteq G$ be its subgroup. We prove that if a smooth del Pezzo surface over an algebraically closed field is $H$-birationally rigid then it is also $G$-birationally rigid, answering a geometric version of Koll\\'{a}r's question in dimension 2 by positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-17T18:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E07",
      "14E05",
      "14E30",
      "14J45",
      "14M22"
    ],
    "keywords": [
      "birational rigidity",
      "smooth del pezzo surface",
      "birationally rigid",
      "finite group",
      "geometric version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}