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arXiv · 2210.15263

A Note On K\"ahler-Ricci Flow on Fano Threefolds

Minghao Miao·Gang Tian
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Abstract

In this note, we show that the solution of K\"ahler-Ricci flow on every Fano threefold from the family No.2.23 in the Mori-Mukai's list develops type II singularity. In fact, we show that no Fano threefold from the family No.2.23 admits K\"ahler-Ricci soliton and the Gromov-Hausdorff limit of the K\"ahler-Ricci flow must be a singular $\mathbb{Q}$-Fano variety. This gives new examples of Fano manifolds of the lowest dimension on which K\"ahler-Ricci flow develops type II singularity.

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Minghao Miao, Gang Tian. 2022-10-27. A Note On K\"ahler-Ricci Flow on Fano Threefolds. https://doi.org/10.1007/s42543-023-00078-0

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