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

Autor: Li, Yan, Tian, Gang, Zhu, Xiaohua
Rok vydání: 2018
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Comment: 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 $G$
Databáze: arXiv