期刊
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
卷 55, 期 1, 页码 1-41出版社
SOC MATHEMATIQUE FRANCE
DOI: 10.24033/asens.2490
关键词
Throughout; we work over a characteristic zero algebraically closed field k
类别
We prove that uniform K-stability is a Zariski open condition in Q-Gorenstein families of Q-Fano varieties and investigate the behavior of the stability threshold in families.
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.
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