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Seminar on Geometric Complex Analysis
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2018/05/28
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Nakamura (Tohoku University)
A generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant (JAPANESE)
Satoshi Nakamura (Tohoku University)
A generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant (JAPANESE)
[ Abstract ]
The existence problem of Kähler Einstein metrics for Fano manifolds was one of the central problems in Kähler Geometry. The vanishing of the Futaki invariant is known as an obstruction to the existence of Kähler Einstein metrics. Generalized Kähler Einstein metrics (GKE for short), introduced by Mabuchi in 2000, is a generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant. In this talk, we give the followings:
(i) The positivity for the Hessian of the Ricci Calabi functional which characterizes GKE as its critical points, and its application.
(ii) A criterion for the existence of GKE on toric Fano manifolds from view points of an algebraic stability and an analytic stability.
The existence problem of Kähler Einstein metrics for Fano manifolds was one of the central problems in Kähler Geometry. The vanishing of the Futaki invariant is known as an obstruction to the existence of Kähler Einstein metrics. Generalized Kähler Einstein metrics (GKE for short), introduced by Mabuchi in 2000, is a generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant. In this talk, we give the followings:
(i) The positivity for the Hessian of the Ricci Calabi functional which characterizes GKE as its critical points, and its application.
(ii) A criterion for the existence of GKE on toric Fano manifolds from view points of an algebraic stability and an analytic stability.
