Title: The K-stability and singularities.

Speaker: Yuji Odaka

Time: Aug 23, 2011 3:30 - 5:00 pm

Venue: Room 1328, Resource Building, Peking University

Abstract: The K-stability is a purely algebro-geometric notion defined for polarized varieties (X,L), which is expected to be equivalent to the existence of constant scalar curvature K"ahler metric with K"ahler class c_1(L). It was introduced by Tian and refined by Donaldson. This opens a way to study the problem of existence of such canonical K"ahler metrics from algebro-geometric standpoint, which I will show.

Regarding to the problem "Concretely when (X,L) is stable?", I will show that criteria should related to singularities at least in two sense:
(1)[Local effect] Bad singularities destabilize polarized varieties.
(2)[Fano case (``global")] Mildness of singularities of subschemes, mainly of anticanonical divisors derives K-stability of almost Fano manifolds.

The study (2) was motivated by and related to the alpha invariant of Tian.