The normalized volume of a singularity is lower semicontinuous

Harold Blum, Yuchen Liu

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We show that in any Q-Gorenstein flat family of klt singularities, normalized volumes are lower semicontinuous with respect to the Zariski topology. A quick consequence is that smooth points have the largest normalized volume among all klt singularities. Using an alternative characterization of K-semistability developed by Li, Liu, and Xu, we show that K-semistability is a very generic or empty condition in any Q-Gorenstein flat family of log Fano pairs.

Original languageEnglish (US)
Pages (from-to)1225-1256
Number of pages32
JournalJournal of the European Mathematical Society
Volume23
Issue number4
DOIs
StatePublished - 2021

Keywords

  • K-stability
  • Normalized volume
  • Singularities

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'The normalized volume of a singularity is lower semicontinuous'. Together they form a unique fingerprint.

Cite this