{
  "abstract": "We study collapsing finite-time singularities of the unnormalized Kähler--Ricci flow on Fano bundles arising in the analytic minimal model program. For a Fano bundle $X^n\\rightarrow Y^m$, we prove a maximal splitting theorem by the Kähler-Ricci flow that every tangent space at a fixed limiting point splits globally as \\((\\C^m,g_{\\rm E},J_0)\\times(Z',d',J')\\). If the fibre has complex dimension one, we prove a global Type-I bound for the full curvature tensor and show that the ambient and intrinsic diameters of every fibre are uniformly comparable to \\(\\sqrt{T-t}\\). Furthermore, every tangent flow at any fixed limiting point is the round shrinking cylinder \\(\\C^m\\times\\PP^1\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02878",
  "author_total": 2,
  "authors": [
    {
      "name": "Wangjian Jian"
    },
    {
      "name": "Jian Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dtv94dvpwc18x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02878",
  "fulltext_url": null,
  "id": "dtv94dvpwc18x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02878",
  "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.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7207531830",
  "pdf_url": "https://arxiv.org/pdf/2609.02878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dtv94dvpwc18x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles",
  "title_text": "Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/dtv94dvpwc18x",
  "venue": "arXiv",
  "versions": []
}