AI 中文总结
该研究针对解析极小模型纲领中的凯勒-里奇流有限时间奇点，在特定假设下证明复二维非坍缩凯勒-里奇流奇点行为的模型，在高维及紧致收缩子情形也获相关结果，完善了相关理论。
AI 中文摘要
我们描述了解析极小模型纲领中出现的凯勒-里奇流的某些有限时间奇点。假设通过全纯映射实现了向渐近锥形凯勒-里奇收缩子的收敛，我们证明，在固定全纯规范下，附近的流在凯勒势层面以收缩子为模型。因此，复二维中每一个非坍缩的凯勒-里奇流穿过奇点的过程都以收缩子-锥-扩张子转变为模型，证实了宋的猜想图景的强形式。我们还在卡拉比 ansatz 下的更高维情形中证明了类似结果，并改进了紧致收缩子情形下的已知结果。这些结果给出了首个小尺度行为被完全描述的穿过锥形奇点的紧致里奇流。
英文摘要
We describe certain finite-time singularities of the Kähler-Ricci flow arising in the analytic minimal model program. Assuming that convergence to an asymptotically conical Kähler-Ricci shrinker is realized by holomorphic maps, we prove that, in a fixed holomorphic gauge, the nearby flow is modeled on the shrinker at the level of Kähler potentials. Consequently, every noncollapsed Kähler-Ricci flow through singularities in complex dimension two is modeled on a shrinker-cone-expander transition, confirming a strong form of Song's conjectural picture. We also show analogous results in higher dimensions under the Calabi ansatz, and improve known results in the compact shrinker case. These give the first compact Ricci flows through conical singularities whose small-scale behavior is fully described.
Comments53 pages, 1 figure. Comments welcome
