{
  "id": "2302.11921",
  "version": "v1",
  "published": "2023-02-23T10:57:07.000Z",
  "updated": "2023-02-23T10:57:07.000Z",
  "title": "Endomorphisms of Fano threefolds and hypersurfaces in arbitrary characteristic",
  "authors": [
    "Tatsuro Kawakami"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $k$ be an algebraically closed field of characteristic $p\\geq 0$. Let $X$ be a smooth Fano threefold over $k$ of Picard number one or a smooth hypersurface over $k$ of dimension bigger than two that admits a non-invertible endomorphism. We assume that the degree of the endomorphism is coprime to $p$ when $p>0$. When $p=0$, it is known that $X$ is isomorphic to the projective space by the work of Amerik-Rovinsky-Van de Ven, Hwang-Mok, Paranjape-Srinivas, and Beauville. In this paper, we generalize this result to arbitrary characteristic. In the proof, we prove that $X$ satisfies the Bott vanishing theorem. This is a new approach even when $p=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-23T10:57:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F17",
      "14J45",
      "14J70",
      "08A35"
    ],
    "keywords": [
      "arbitrary characteristic",
      "smooth fano threefold",
      "picard number",
      "smooth hypersurface",
      "dimension bigger"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}