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

Abstract

We prove that the Gromov–Hausdorff limit of Kähler–Ricci flow on a ${\textbf{G}}$-spherical Fano manifold X is a ${\textbf{G}}$-spherical ${\mathbb {Q}}$-Fano variety $X_{\infty }$, which admits a (singular) Kähler–Ricci soliton. Moreover, the ${\textbf{G}}$-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 ${\textbf{G}}$.

Keywords

${\textbf{G}}$-Spherical variety / Kähler–Ricci flow / Equivariant ${\mathbb {C}}^*$-degeneration / Primary: 53E20 / 53C25 / Secondary: 32Q20 / 53C30 / 14L10

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Funding

National Key Research and Development Program of China(No. 2022YFA1005501)

National Natural Science Foundation of China(NSFC 12031017)

National Key R &D Program of China(2020YFA0712800)

RIGHTS & PERMISSIONS

Peking University