{
  "abstract": "Let $F$ be a projective variety, let $H$ be a normally generated line bundle on $F$, and let $X\\in |H^{\\otimes d}|$ be a general projective variety. We establish a uniform criterion, formulated in terms of the graded Betti numbers of the section ring $R(F,H)$, that provides sufficient conditions for every automorphism of $X$ to extend to an automorphism of $F$. This extends the classical results of Matsumura-Monsky on automorphisms of hypersurfaces in projective spaces to a broader class of polarized varieties $(F,H)$, including rational homogeneous varieties of Picard number one, smooth Fano threefolds with their anticanonical polarization, and examples of hyperkähler and Calabi-Yau varieties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00709",
  "author_total": 1,
  "authors": [
    {
      "name": "Ana Quedo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvksk6db7nw5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00709",
  "fulltext_url": null,
  "id": "fvksk6db7nw5d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00709",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7215811984",
  "pdf_url": "https://arxiv.org/pdf/2610.00709",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvksk6db7nw5d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00709",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00709"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Automorphisms of hypersurfaces in polarized varieties",
  "title_text": "Automorphisms of hypersurfaces in polarized varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/fvksk6db7nw5d",
  "venue": "arXiv",
  "versions": []
}