{
  "id": "2404.04790",
  "version": "v1",
  "published": "2024-04-07T02:39:04.000Z",
  "updated": "2024-04-07T02:39:04.000Z",
  "title": "Global $F$-regularity for weak del Pezzo surfaces",
  "authors": [
    "Tatsuro Kawakami",
    "Hiromu Tanaka"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $k$ be an algebraically closed field of characteristic $p>0$. Let $X$ be a normal projective surface over $k$ with canonical singularities whose anti-canonical divisor is nef and big. We prove that $X$ is globally $F$-regular except for the following cases: (1) $K_X^2=4$ and $p=2$, (2) $K_X^2=3$ and $p \\in \\{2, 3\\}$, (3) $K_X^2=2$ and $p \\in \\{2, 3\\}$, (4) $K_X^2=1$ and $p \\in \\{2, 3, 5\\}$. For each degree $K_X^2$, the assumption of $p$ is optimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-07T02:39:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "13A35"
    ],
    "keywords": [
      "weak del pezzo surfaces",
      "regularity",
      "normal projective surface",
      "characteristic",
      "algebraically closed field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}