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 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 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.

6 pages, comments are welcome!

References in corpus (2)

• The existence of the Kähler-Ricci soliton degeneration
• K-stability of Gorenstein Fano group compactifications with rank two