Kähler–Ricci Flow on \({\textbf{G}}\)-Spherical Fano Manifolds

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