A Note on Kähler–Ricci Flow on Fano Threefolds

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 $\mathbb {Q}$-Fano variety. This gives new examples of Fano manifolds of the lowest dimension on which Kähler–Ricci flow develops type II singularity.