OPENNESS OF UNIFORM K-STABILITY IN FAMILIES OF Q-FANO VARIETIES

被引：18

作者：

Blum, Harold ^{[1
]}

Liu, Yuchen ^{[2
]}

机构：

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[2] Yale Univ, Dept Math, New Haven, CT 06511 USA

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2022年 / 55卷 / 01期

基金：

美国国家科学基金会;

关键词：

Throughout; we work over a characteristic zero algebraically closed field k; KAHLER-EINSTEIN METRICS; GREATEST LOWER BOUNDS; SCALAR CURVATURE; RICCI CURVATURE; OKOUNKOV BODIES; MODULI SPACES; INVARIANTS; VALUATION;

D O I：

10.24033/asens.2490

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1 / 41

页数：41

共 57 条

[1] Variation of Log Canonical Thresholds in Linear Systems [J].