K\"ahler-Ricci flow on $\mathbf G$-spherical Fano manifolds

Feng Wang; Xiaohua Zhu

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arXiv · 2305.05366

K\"ahler-Ricci flow on $\mathbf G$-spherical Fano manifolds

Feng Wang·Xiaohua Zhu

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Abstract

We prove that the Gromov-Hausdorff limit of K\"ahler-Ricci flow on a $\mathbf G$-spherical Fano manifold $X$ is a $\mathbf G$-spherical $\mathbb Q$-Fano variety $X_{\infty}$, which admits a (singular) K\"ahler-Ricci soliton. Moreover, the $\mathbf G$-spherical variety structure of $X_{\infty}$ can be constructed as a center of torus $\mathbb C^*$-degeneration of $X$ induced by an element in the Lie algebra of Cartan torus of $\mathbf G$.

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BibTeX RIS

Feng Wang, Xiaohua Zhu. 2023-05-09. K\"ahler-Ricci flow on $\mathbf G$-spherical Fano manifolds. https://arxiv.org/abs/2305.05366

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