On the sharpness of Tian's criterion for K-stability

2019/03/12 by Liu, Yuchen, Zhuang, Ziquan · 1 citation
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.04719

Abstract

Tian's criterion for K-stability states that a Fano variety of dimension n whose alpha invariant is greater than (n)/(n+1) is K-stable. We show that this criterion is sharp by constructing singular Fano varieties with alpha invariants (n)/(n+1) that are not K-polystable for sufficiently large n. We also construct K-unstable Fano varieties with alpha invariants (n-1)/(n).

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