{
  "abstract": "We establish the following Miyaoka-Yau inequality for any $n$-dimensional klt Fano variety $X$, possibly K-unstable, in terms of its delta invariant: \\[\\left(2(n+1)\\widehat{c}_2(X)-n c_1(X)^2\\right)\\cdot c_1(X)^{n-2} \\ge -n \\left(1-\\min\\{1,δ(X)\\}\\right)^2 \\cdot c_1(X)^n.\\] Moreover, if equality holds in this inequality, then there exist a finite quasi-étale cover $\\widehat{X} \\to X$ and a positive integer $p$ such that $\\widehat{X} \\cong \\mathbb{P}(1,\\ldots, 1, p)$. We also discuss the relationship between Donaldson's conjecture and the Miyaoka-Yau inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.25181",
  "author_total": 2,
  "authors": [
    {
      "name": "Tomoyuki Hisamoto"
    },
    {
      "name": "Masataka Iwai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fcysqg082r8gp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.25181",
  "fulltext_url": null,
  "id": "fcysqg082r8gp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.25181",
  "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"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7171676321",
  "pdf_url": "https://arxiv.org/pdf/2607.25181",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fcysqg082r8gp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2607.25181",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.25181"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Miyaoka-Yau inequality and the delta invariant for Fano varieties I -klt Fano case-",
  "title_text": "The Miyaoka-Yau inequality and the delta invariant for Fano varieties I -klt Fano case-",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/fcysqg082r8gp",
  "venue": "arXiv",
  "versions": []
}