{
  "abstract": "We investigate birational automorphisms of hypersurfaces that preserve the projection from a point. Let $V \\subset \\mathbb{P}^{n+1}$ be an irreducible hypersurface of degree $d \\ge 3$ with $\\dim \\mathrm{Sing}(V) \\le n-2$, and let $π_P : V \\dashrightarrow \\mathbb{P}^n$ denote the projection from a point $P \\in \\mathbb{P}^{n+1} \\setminus \\mathrm{Sing}(V)$. Assume moreover that if $d = 3$ then $P \\notin V$. We prove that any $σ\\in \\mathrm{Bir}(V)$ satisfying $π_P \\circ σ= π_P$ extends uniquely to a projective transformation of $\\mathbb{P}^{n+1}$. By combining the above projective lifting theorem with the theory of complex reflection groups, we investigate Galois and quasi-Galois points for the Fermat variety $F_d^n \\subset \\mathbb P^{n+1}$ of dimension $n$ and degree $d$. We show that, for $d \\ge 4$, $F_d^n$ has exactly $n+2$ Galois points and, in addition, $d(n+2)(n+1)/2$ quasi-Galois points. When $d=3$, $F_3^n$ has exactly $n+2$ outer Galois points.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09331",
  "author_total": 2,
  "authors": [
    {
      "name": "Kei Miura"
    },
    {
      "name": "Takeshi Takahashi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55dfgdynqgybw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09331",
  "fulltext_url": null,
  "id": "55dfgdynqgybw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09331",
  "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": "W7220922196",
  "pdf_url": "https://arxiv.org/pdf/2610.09331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55dfgdynqgybw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Projective Lifting Theorem, Complex Reflection Groups, and Quasi-Galois Points for Fermat Varieties",
  "title_text": "Projective Lifting Theorem, Complex Reflection Groups, and Quasi-Galois Points for Fermat Varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/55dfgdynqgybw",
  "venue": "arXiv",
  "versions": []
}