{
  "abstract": "In this paper, building on our previous Sylow criteria, we establish small-subgroup criteria of liftability and $F$-liftability for the linear automorphism group $G$ of smooth hypersurfaces $X$ over algebraically closed field of characteristic zero. When $\\mathrm{dim} X = p-2$ for some odd prime $p$, we prove that ($F$-)liftability of any finite subgroup of $G$ can be tested on its $p$-subgroups of order at most $p^2$. When $X$ is a degree $p$ hypersurface of dimension $2p-2$, we prove that ($F$-)liftability of $G$ can be tested on all its $p$-subgroups of order at most $p^3$, which is sharp for $p\\geq5$. When $p=3$, this bound improves to $9$, giving the corresponding criteria for smooth cubic fourfolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15613",
  "author_total": 2,
  "authors": [
    {
      "name": "Baiting Xie"
    },
    {
      "name": "Zhiwei Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9x24g2kmpv8pg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15613",
  "fulltext_url": null,
  "id": "9x24g2kmpv8pg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15613",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213287709",
  "pdf_url": "https://arxiv.org/pdf/2609.15613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9x24g2kmpv8pg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15613"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Small-Subgroup Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces",
  "title_text": "Small-Subgroup Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/9x24g2kmpv8pg",
  "venue": "arXiv",
  "versions": []
}