Vortrag: Volume and stability of singularities

Speaker: Chenyang Xu, Beijing International Center for Mathematical Research

Abstract: One guiding principal for the class of kawamata log terminal

(klt) singularities is that it is the local analogue of Fano varieties.

In this talk, I will discuss our work (joint with Chi Li) on establishing an algebraic stability theory, which is the analogue to the K-stability of Fano varieties, for a klt singularity. This is achieved by using Chi Li's definition of normalised volumes. As an application, we prove that the intermediate semistable cone of the metric tangent cone of a klt singularity appearing on the GH limit of Kahler-Einstein Fano manifolds is only determined by the algebraic structure of the singularity but independent of the local metric, which confirms a conjecture by Donaldson-Sun. If time permits, I will discuss other applications of this, e.g. constructing KE metric on Fano manifolds etc.