{
  "abstract": "The analytic minimal model program proposed in \\cite{SongTianSingularities, JST} seeks to describe the birational transitions and fibre collapsing of the Kähler--Ricci flow through the geometry of its singularities. A fundamental conjecture of \\cite{JST} predicts Type I bounds for the scalar curvature and diameter of every fibre contratced by the limiting cohomological class at the finite singular time. This paper is a continuation of \\cite{Splitting} that establishes the Type I conjecture for collapsing solutions on Fano bundles with arbitrary smooth Fano fibres. If the fibre admits a smooth Kähler-Einstein metric, the Type I bound holds for the full curvature tensor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20513",
  "author_total": 2,
  "authors": [
    {
      "name": "Wangjian Jian"
    },
    {
      "name": "Jian Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1tavkrfawc7b7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20513",
  "fulltext_url": null,
  "id": "1tavkrfawc7b7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20513",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7213591134",
  "pdf_url": "https://arxiv.org/pdf/2609.20513",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1tavkrfawc7b7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20513",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20513"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II",
  "title_text": "Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/1tavkrfawc7b7",
  "venue": "arXiv",
  "versions": []
}