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Tuesday Seminar on Topology
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2017/01/10
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Shunsuke Saito (The University of Tokyo)
Stability of anti-canonically balanced metrics (JAPANESE)
Shunsuke Saito (The University of Tokyo)
Stability of anti-canonically balanced metrics (JAPANESE)
[ Abstract ]
Donaldson introduced "anti-canonically balanced metrics" on Fano manifolds, which is a finite dimensional analogue of Kähler-Einstein metrics. It is proved that anti-canonically balanced metrics are critical points of the quantized Ding functional.
We first study the slope at infinity of the quantized Ding functional along Bergman geodesic rays. Then, we introduce a new algebro-geometric stability of Fano manifolds based on the slope formula, and show that the existence of anti-canonically balanced metrics implies our stability. The relationship between the stability and others is also discussed.
This talk is based on a joint work with R. Takahashi (Tohoku Univ).
Donaldson introduced "anti-canonically balanced metrics" on Fano manifolds, which is a finite dimensional analogue of Kähler-Einstein metrics. It is proved that anti-canonically balanced metrics are critical points of the quantized Ding functional.
We first study the slope at infinity of the quantized Ding functional along Bergman geodesic rays. Then, we introduce a new algebro-geometric stability of Fano manifolds based on the slope formula, and show that the existence of anti-canonically balanced metrics implies our stability. The relationship between the stability and others is also discussed.
This talk is based on a joint work with R. Takahashi (Tohoku Univ).
