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arXiv · 2609.02878

Finite-Time Singularities of the K\"ahler--Ricci Flow on Fano Bundles

Wangjian Jian·Jian Song
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Abstract

We study collapsing finite-time singularities of the unnormalized K\"ahler--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 K\"ahler-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 \(\C^m\times\PP^1\).

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Wangjian Jian, Jian Song. 2026-09-02. Finite-Time Singularities of the K\"ahler--Ricci Flow on Fano Bundles. https://arxiv.org/abs/2609.02878

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