Tuesday Seminar on Topology

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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)
[ 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).