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 language | English (US) |
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Pages (from-to) | 1225-1256 |
Number of pages | 32 |
Journal | Journal of the European Mathematical Society |
Volume | 23 |
Issue number | 4 |
DOIs | |
State | Published - 2021 |
Keywords
- K-stability
- Normalized volume
- Singularities
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics