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Original Article

A Note on Kähler–Ricci Flow on Fano Threefolds

Department of Mathematics, Nanjing University, Nanjing 210093, China
BICMR and SMS, Peking University, Beijing 100871, China
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Abstract

In this note, we show that the solution of Kähler–Ricci flow on every Fano threefold from Family No. 2.23 in the Mori–Mukai’s list develops type Ⅱ singularity. In fact, we show that no Fano threefold from Family No. 2.23 admits Kähler–Ricci soliton and the Gromov–Hausdorff limit of the Kähler–Ricci flow must be a singular Q -Fano variety. This gives new examples of Fano manifolds of the lowest dimension on which Kähler–Ricci flow develops type Ⅱ singularity.

Keywords

Kähler–Ricci solitonK-stabilityFano threefoldKähler–Ricci flow

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Peking Mathematical Journal
Volume 8 Issue 1,
March 2025
Pages 191-199
DOI: 10.1007/s42543-023-00078-0

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Cite this article:
Miao, M., Tian, G. A Note on Kähler–Ricci Flow on Fano Threefolds. Peking Math J 8, 191-199 (2025). https://doi.org/10.1007/s42543-023-00078-0

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Received: 06 December 2022
Revised: 19 June 2023
Accepted: 25 August 2023
Published: 28 September 2023
© Peking University 2023