Geometry Colloquium

Seminar information archive ~05/21Next seminarFuture seminars 05/22~

Date, time & place Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.)

2015/04/24

10:00-11:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Kento Fujita (Kyoto University)
On K-stability and the volume functions of Q-Fano varieties (JAPANESE)
[ Abstract ]
For Fano manifolds X, it is known that X admits K\"ahler-Einstein metrics if and only if the polarized pair
(X, -K_X) is K-polystable. In this talk, I will introduce a new effective stability named "divisorial stability" for Fano manifolds, which is weaker than K-stability and stronger than slope stability along divisors. I will show that:
1. We can easily test divisorial stability via the volume functions.
2. There is a relationship between divisorial stability and the structure property of Okounkov bodies of anti-canonical divisors.
3. For toric Fano manifolds, the existence of K\"ahler-Einstein metrics is equivalent to divisorial semistability.