ON THE K-STABILITY OF FANO VARIETIES AND ANTICANONICAL DIVISORS

被引：75

作者：

Fujita, Kento ^{[1
]}

Odaka, Yuji ^{[2
]}

机构：

[1] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan

[2] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

来源：

TOHOKU MATHEMATICAL JOURNAL | 2018年 / 70卷 / 04期

关键词：

Fano varieties; K-stability; Kahler-Einstein metrics; KAHLER-EINSTEIN METRICS; COMPACT MODULI SPACES; SCALAR CURVATURE; MANIFOLDS; LIMITS; BOUNDS;

D O I：

10.2748/tmj/1546570823

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition in terms of certain anti-canonical Q-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that it is at least a sufficient condition and also related to the Berman-Gibbs stability. We also give another algebraic proof of the K-stability of Fano varieties which satisfy Tian's alpha invariants condition.

引用

页码：511 / 521

页数：11

共 50 条

[31] Finite generation for valuations computing stability thresholds and applications to K-stability
Liu, Yuchen
Xu, Chenyang
Zhuang, Ziquan
ANNALS OF MATHEMATICS, 2022, 196 (02) : 507 - 566
[32] Uniqueness of K-polystable degenerations of Fano varieties
Blum, Harold
Xu, Chenyang
ANNALS OF MATHEMATICS, 2019, 190 (02) : 609 - 656
[33] On K-stability of some del Pezzo surfaces of Fano index 2
Liu, Yuchen
Petracci, Andrea
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2022, 54 (02) : 517 - 525
[34] K-stability of Fano threefolds of rank 3 and degree 14
Belousov G.
Loginov K.
ANNALI DELL'UNIVERSITA' DI FERRARA, 2024, 70 (3) : 1093 - 1114
[35] On the K-stability of complete intersections in polarized manifolds
Arezzo, Claudio
Della Vedova, Alberto
ADVANCES IN MATHEMATICS, 2011, 226 (06) : 4796 - 4815
[36] Birational Superrigidity and K-Stability of Projectively Normal Fano Manifolds of Index One
Suzuki, Fumiaki
MICHIGAN MATHEMATICAL JOURNAL, 2021, 70 (04) : 779 - 792
[37] K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces
Kim, In-Kyun
Okada, Takuzo
Won, Joonyeong
FORUM OF MATHEMATICS SIGMA, 2023, 11
[38] K-STABILITY OF CUBIC THREEFOLDS
Liu, Yuchen
Xu, Chenyang
DUKE MATHEMATICAL JOURNAL, 2019, 168 (11) : 2029 - 2073
[39] TITS BUILDINGS AND K-STABILITY
Codogni, Giulio
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2019, 62 (03) : 799 - 815
[40] On K-stability of finite covers
Dervan, Ruadhai
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2016, 48 : 717 - 728

← 1 2 3 4 5 →