Calendar
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
Seminar webpage: https://sites.google.com/view/rutgersgeometrytopologyseminar/home
Abstract:
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.
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.
