{
  "abstract": "Let $C$ be a reduced plane curve of degree $n$ with only ADE singularities. Using Kähler-Einstein metrics, Kobayashi proved an upper bound, in terms of $n$, for a sum of local invariants of the singular points of $C$. For even $n$ this bound had been obtained earlier by Hirzebruch and Ivinskis. Curves of even degree for which equality holds are called Miyaoka-Kobayashi curves, and the only known examples are three types of plane sextics. We show that there are no Miyaoka--Kobayashi curves of degree $8$, and additionally that a Miyaoka-Kobayashi curve of degree $10$ cannot be free. The key new ingredient is a new linear constraint on the singularities of such curves, obtained by differentiating Langer's orbifold Bogomolov-Miyaoka-Yau inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28135",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexandru Dimca"
    },
    {
      "name": "Piotr Pokora"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aynjfnrmxrsqj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28135",
  "fulltext_url": null,
  "id": "aynjfnrmxrsqj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28135",
  "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": "W7223142283",
  "pdf_url": "https://arxiv.org/pdf/2610.28135",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aynjfnrmxrsqj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28135",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28135"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "There are no Miyaoka--Kobayashi octics",
  "title_text": "There are no Miyaoka--Kobayashi octics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/aynjfnrmxrsqj",
  "venue": "arXiv",
  "versions": []
}