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arXiv · 1807.09167

Singular limits of K\"ahler-Ricci flow on Fano $G$-manifolds

Yan Li·Gang Tian·Xiaohua Zhu
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Abstract

In this paper, we prove that any solution of K\"ahler-Ricci flow on a Fano compactification $M$ of semisimple complex Lie group, is of type II, if $M$ admits no K\"ahler-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 K\"ahler-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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Yan Li, Gang Tian, Xiaohua Zhu. 2018-07-24. Singular limits of K\"ahler-Ricci flow on Fano $G$-manifolds. https://arxiv.org/abs/1807.09167

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