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SUMMARY:Discreteness of local volumes - Chenyang Xu (Princeton University)
DTSTART:20240517T104500Z
DTEND:20240517T114500Z
UID:TALK214453@talks.cam.ac.uk
DESCRIPTION:(Joint with Ziquan Zhuang) The concept of local volume of a kl
 t singularity\, which is the infimum of normalized volumes of all valuatio
 ns centered at the singularity\, plays a central role in the local stabili
 ty theory. The Stable Degeneration Theorem says any klt singularity admits
  a volume preserved degeneration to a K-semistable log Fano cone singulari
 ty. In this talk\, I will show that all K-semistable log Fano cone singula
 rities with volume bounded from below are bounded. As a consequence\, this
  implies that the set of normalized volumes of all klt singularities has 0
  as its only accumulation point.&nbsp\;&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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