Finite Time Type I Singularities of the Kähler Ricci Flow

Abstract

We prove the Feldman--Ilmanen--Knopf conjecture for finite time Type I singularities of the Kähler--Ricci flow. More precisely, for any compact Kähler manifold $Y$ and its blow-up $π:\operatorname{Bl}_pY\longrightarrow Y$, if $[ω_0]-Tc_1(M)=π^*[ω_Y]$, then any Type I parabolic blow-up limit of the Kähler Ricci flow along the exceptional divisor is the FIK shrinker $\operatorname{Tot}(\mathcal{O}_{\mathbb{P}^{n-1}}(-1))$.

Disclosure

“grateful to Zhixian Zhu for many helpful discus- sions and valuable advice on the algebraic-geometric aspects of this work. The main ideas, arguments, and overall direction of the paper were developed by the authors. AI tools (Chat GPT and Deepseek) were used during the preparation of the manuscript as technical assistants for checking arguments, locating relevant references, and improving the exposi- tion. In particular, AI tools suggested estimating the length of a relative extrema”

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2026-08-23T05:21:22.482727Z

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