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Vortrag: Volume and stability of singularities

When Sep 21, 2017
from 10:00 AM to 04:00 PM
Where Mathematical Institute, Seminar room 403
Contact Name
Contact Phone +49 (0)761 203-97362
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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.