Year: 2026
Type: preprint
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 \(\C^m\times\PP^1\).
Source: arXiv (Cornell University)
Authors: Jian, Wangjian, Song, Jian
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207531830