Title:“Special Test Configurations and K-stability of Fano Manifold”
Speaker: Chi Li, Princeton University
Date: Tuesday, January 31, 2012
Time: 10:30am – 12:00pm
Place: Seminar Room 313, Simons Center
Abstract:
In order to find out whether there is a Kahler-Einstein metric on any Fano manifold, special degenerations and generalized Futaki invariant were introduced by Tian to test properness of the energy functional. Motivated by compactness results from Riemannian geometry, Tian required such degeneration has normal central fibre. Donaldson considered more general test configurations with no constraint on the central fibre. I will talk about recent joint work with Chenyang Xu. We use Minimal Model Program from birational algebraic geometry to simplify any given test configuration. In particular, when the Picard number is 1, we prove any test configuration can be reduced to a special degeneration with smaller generalized Futaki invariant.