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

@misc{jian2026finitetime,
  title = {{Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II}},
  author = {Wangjian Jian and Jian Song},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20513},
  eprint = {2609.20513},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20513},
  note = {CC0},
}

TY  - UNPB
TI  - Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
AU  - Wangjian Jian
AU  - Jian Song
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20513
UR  - https://arxiv.org/abs/2609.20513
AB  - 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.
ER  -