OPENNESS OF UNIFORM K-STABILITY IN FAMILIES OF Q-FANO VARIETIES

Harold Blum, Yuchen Liu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We show that uniform K-stability is a Zariski open condition in Q-Gorenstein families of Q-Fano varieties. To prove this result, we consider the behavior of the stability threshold in families. The stability threshold (also known as the delta-invariant) is a recently introduced invariant that is known to detect the K-semistability and uniform K-stability of a Q-Fano variety. We show that the stability threshold is lower semicontinuous in families and provides an interpretation of the invariant in terms of the K-stability of log pairs.

Original languageEnglish (US)
Pages (from-to)1-41
Number of pages41
JournalBulletin de la Societe Mathematique de France
Volume55
DOIs
StatePublished - 2022

ASJC Scopus subject areas

  • General Mathematics

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