ON the SHARPNESS of TIAN'S CRITERION for K-STABILITY

Yuchen Liu, Ziquan Zhuang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Tian's criterion for K-stability states that a Fano variety of dimension n whose alpha invariant is greater than is K-stable. We show that this criterion is sharp by constructing n-dimensional singular Fano varieties with alpha invariants that are not K-polystable for sufficiently large n. We also construct K-unstable Fano varieties with alpha invariants.

Original languageEnglish (US)
Pages (from-to)41-73
Number of pages33
JournalNagoya Mathematical Journal
Volume245
DOIs
StatePublished - Mar 23 2022

ASJC Scopus subject areas

  • Mathematics(all)

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