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Topology/Geometry Seminar

Kaehler-Ricci flow on Fano horosymmetric manifolds

Xiaohua Zhu (Peking University)

Location:  Hill Center, Room 705
Date & time: Tuesday, 24 January 2023 at 4:00PM - 5:00PM

I will talk about a recent work jointly with Tian on Kaehler-Ricci flow on Fano G-manifolds. We prove that on a Fano G-manifold, the Gromov-Hausdorff limit of Kaehler-Ricci flow with initial metric in \(2\pi c_1(M)\) must be a Q-Fano horosymmetric variety which admits a singular Keahler-Ricci soliton. Moreover, we show that the complex structure of limit variety can be constructed by a \(C^*\)-degeneration induced by an element in the Cartan torus Lie algebra of G. A similar result can be also proved for Kaehler-Ricci flows on any Fano horosymmetric manifolds.