Volume and stability of singularities

Mardi 6 mars 2018 14:15-15:15 - Chenyang Xu - Beijing International Center of Mathematical Research

Résumé : One guiding principle 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 on the ’non-archimedean link’. The conjectural picture can be considered as a purely local construction which algebrizes the metric tangent cone in complex geometry. As an application, we solve Donaldson-Sun’s conjecture.

Lieu : IMO Bât. 307, salle 3L15

Volume and stability of singularities  Version PDF