论文标题
fano $ g $ -Manifolds的Kähler-Ricci流的骨对称限制
Horosymmetric limits of Kähler-Ricci flow on Fano $G$-manifolds
论文作者
论文摘要
在本文中，我们证明，在fano $ \ mathbf g $ -manifold $（m，j）$上，Kähler-ricci的Gromov-Hausdorff限制限制了$2πc_1（m）$的初始度量，必须是$ \ \ mathbb Q $ -Fano-fano horosmmetric Valter $ m_ $ m_ $ m_ $ m_ $ m_ \ m_ \ forty $ solit-yrit-sing a the n of the n the n thing a the n thing a the n of thing a dembir k.此外，$ m_ \ infty $是$ \ mathbb c^*$ - $ m $的$ \ mathbb c^*$ - 在$ \ mathbf g $的cartan torus lie代数中引起的$ m $变性。对于任何FANO骨对称歧管上的Kähler-Ricci流也可以证明类似的结果。作为一个应用程序，我们将先前的结果推广到fano $ \ mathbf g $ -manifolds上的Kähler-Icci流向fano Horosymmetric歧管上的II型奇异性。
In this paper, we prove that on a Fano $\mathbf G$-manifold $(M,J)$, the Gromov-Hausdorff limit of Kähler-Ricci flow with initial metric in $2πc_1(M)$ must be a $\mathbb Q$-Fano horosymmetric variety $M_\infty$, which admits a singular Kähler-Ricci soliton. Moreover, $M_\infty$ is a limit of $\mathbb C^*$-degeneration of $M$ induced by an element in the Lie algebra of Cartan torus of $\mathbf G$. A similar result can be also proved for Kähler-Ricci flows on any Fano horosymmetric manifolds. As an application, we generalize our previous result about the type II singularity of Kähler-Ricci flows on Fano $\mathbf G$-manifolds to Fano horosymmetric manifolds.
