发表机构
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Department of Mathematics, Rutgers University（中国科学院数学与系统科学研究院; 罗格斯大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对解析极小模型纲领中的法诺丛，证明其未归一化凯勒-里奇流的有限时间奇点相关分裂定理、曲率界及切流结构，完善了凯勒-里奇流的奇点理论。
AI 中文摘要
我们研究解析极小模型纲领中产生的法诺丛上未归一化凯勒-里奇流的坍缩有限时间奇点。对于法诺丛$X^n\rightarrow Y^m$，我们通过凯勒-里奇流证明了一个极大分裂定理：每个固定极限点处的切空间整体分裂为$(\mathbb{C}^m,g_{\rm E},J_0)\times(Z',d',J')$。若纤维的复维数为1，我们证明了全曲率张量的全局I型界，并表明每个纤维的环境直径与内在直径均与$\sqrt{T-t}$一致可比。此外，每个固定极限点处的切流均为圆收缩圆柱$\mathbb{C}^m\times\mathbb{P}^1$。
英文摘要
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 \(\C^m\times\PP^1\).
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