{
  "abstract": "We obtain inequalities for isolated $cD_n, cE_6, cE_7$ and $cE_8$ singularities, analogues of the $4μ^2/(n+1)$-inequality for isolated $cA_n$ singularity in \\cite{KOP}. These inequalities are sharp. This enables us to prove the birational rigidity of certain families of Fano $3$-fold weighted hypersurfaces, which contain only terminal quotient singularities and one $cD_n$ singularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28372",
  "author_total": 3,
  "authors": [
    {
      "name": "Chi-Kang Chang"
    },
    {
      "name": "Jheng-Jie Chen"
    },
    {
      "name": "Takuzo Okada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53vt8my83c0dq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28372",
  "fulltext_url": null,
  "id": "53vt8my83c0dq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28372",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204790760",
  "pdf_url": "https://arxiv.org/pdf/2608.28372",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53vt8my83c0dq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2608.28372",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28372"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Local inequalities for $cD$ and $cE$ singularities",
  "title_text": "Local inequalities for cD and cE singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/53vt8my83c0dq",
  "venue": "arXiv",
  "versions": []
}