Singular limits of Kähler-Ricci flow on Fano $G$-manifolds

Abstract

In this paper, we prove that any solution of Kähler-Ricci flow on a Fano compactification $M$ of semisimple complex Lie group, is of type II, if $M$ admits no Kähler-Einstein metrics. As an application, we found two Fano compactifications of ${\mathrm{SO}}_4(\mathbb{C})$ and one Fano compactification of ${\mathrm{Sp}}_4(\mathbb{C})$, on which the Kähler-Ricci flow will develop singularities of type II. To the authors' knowledge, these are the first examples of Ricci flow with singularities of type II on Fano manifolds in the literature.

We added an appendix in Section 7 to prove Theorem 7.3 which is a generalization of Theorem 1.1 for any complex reductive Lie group $G$

References in corpus (3)

• Space of Ricci flows (II)
• K-Stability of Fano spherical varieties
• Kähler-Einstein metrics on group compactifications

Cited by in corpus (4)

• Examples of K-unstable Fano manifolds
• Tian's partial $C^0$-estimate implies Hamilton-Tian's conjecture
• Kähler-Ricci flow for deformed complex structures
• K-stability and polystable degenerations of polarized spherical varieties