Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles

@misc{jian2026finitetime,
  title = {{Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles}},
  author = {Wangjian Jian and Jian Song},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02878},
  eprint = {2609.02878},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02878},
  note = {CC0},
}

TY  - UNPB
TI  - Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles
AU  - Wangjian Jian
AU  - Jian Song
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02878
UR  - https://arxiv.org/abs/2609.02878
AB  - 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→ 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_E,J_0)×(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 √(T−t). Furthermore, every tangent flow at any fixed limiting point is the round shrinking cylinder C^m×PP^1.
ER  -