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ON THE SHARPNESS OF TIAN’S CRITERION FOR K-STABILITY
Nagoya Mathematical Journal ( IF 0.8 ) Pub Date : 2020-10-23 , DOI: 10.1017/nmj.2020.28
YUCHEN LIU 1 , ZIQUAN ZHUANG 2
Affiliation  

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 ${(n-1)}{/n}$ .



中文翻译:

关于 K 稳定性 Tian 判据的锐度

Tian 的 K 稳定性判据表明,α 不变量大于 ${n}{/(n+1)}$ 的维数n的 Fano 变体是 K 稳定的。我们通过构造具有 alpha 不变量 ${n}{/(n+1)}$ 的n维奇异 Fano 变体来证明这个标准是尖锐的,这些变体对于足够大的n不是 K-polystable 。 我们还构建了具有 alpha 不变量${(n-1)}{/n}$ 的 K-不稳定 Fano 变体。

更新日期:2020-10-23
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