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arXiv · 2608.17458

Finite Time Type I Singularities of the K\"ahler Ricci Flow

Tongxin Xu·Zhenlei Zhang
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Abstract

We prove the Feldman--Ilmanen--Knopf conjecture for finite time Type I singularities of the K\"ahler--Ricci flow. More precisely, for any compact K\"ahler manifold $Y$ and its blow-up $\pi:\operatorname{Bl}_pY\longrightarrow Y$, if $[\omega_0]-Tc_1(M)=\pi^*[\omega_Y]$, then any Type I parabolic blow-up limit of the K\"ahler Ricci flow along the exceptional divisor is the FIK shrinker $\operatorname{Tot}(\mathcal{O}_{\mathbb{P}^{n-1}}(-1))$.

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Tongxin Xu, Zhenlei Zhang. 2026-08-18. Finite Time Type I Singularities of the K\"ahler Ricci Flow. https://arxiv.org/abs/2608.17458

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