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Volume and stability of singularities

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Chenyang Xu (Peking/Paris/MIT) - Seminar Algebraic Geometry (SAG)

  • Seminar
When Apr 19, 2018
from 10:30 am to 11:30 am
Where Bonn, Hörsaal MPI, Vivatsgasse 7
Contact Name Sachinidis
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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.