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ON THE SHARPNESS OF TIAN’S CRITERION FOR K-STABILITY
Published online by Cambridge University Press: 23 October 2020
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 n-dimensional 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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- © Foundation Nagoya Mathematical Journal, 2020
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