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

2018/07/24 by Li, Yan, Tian, Gang, Zhu, Xiaohua · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.09167

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 SO₄(ℂ) and one Fano compactification of Sp₄(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.

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