{
  "abstract": "We use the Kähler-Ricci flow to give alternate proofs of several known Miyaoka-Yau inequalities and slope semi-stabilities, in particular, for the case of compact Kähler manifolds with semi-ample canonical line bundles and K-semistable Fano manifolds. Moreover, when the canonical line bundle is semi-ample, and the Kodaira dimension is $n-1$, we prove the Miyaoka-Yau quantity is equal to the intersection of the Weil-Petersson metric and the Fubini-Study metric on the canonical model. Consequently, equality holds in the Miyaoka-Yau inequality if and only if the pluricanonical map is a holomorphic fibre bundle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06451",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Bednarek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7vdh9ms550nv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06451",
  "fulltext_url": null,
  "id": "d7vdh9ms550nv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06451",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7212072443",
  "pdf_url": "https://arxiv.org/pdf/2609.06451",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7vdh9ms550nv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06451",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06451"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Miyaoka-Yau Inequalities and Weil-Petersson Metrics",
  "title_text": "On Miyaoka-Yau Inequalities and Weil-Petersson Metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/d7vdh9ms550nv",
  "venue": "arXiv",
  "versions": []
}