ABOUT J-FLOW, J-BALANCED METRICS, UNIFORM J-STABILITY AND K-STABILITY

被引：1
作者：
Hashimoto, Yoshinori [1 ,2 ]
Keller, Julien [2 ]
机构：
[1] Data4Cs KK, Minato Ku, 5-2-32 Minamiazabu, Tokyo, Japan
[2] Aix Marseille Univ, Inst Math Marseille, Cent Marseille, CNRS,UMR 7373, F-13453 Marseille, France
来源：
ASIAN JOURNAL OF MATHEMATICS | 2018年 / 22卷 / 03期
关键词：
J-flow; balanced metrics; uniform K-stability; J-stability; constant scalar curvature Kahler metrics; MABUCHI ENERGY; NUMERICAL ALGORITHM; KAHLER-MANIFOLDS; CONVERGENCE; VARIETIES; CURVATURE; CRITERION; SURFACES; THEOREM;
D O I：
10.4310/AJM.2018.v22.n3.a1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
From the work of Dervan-Keller [DK15], there exists a quantization of the critical equation for the J-flow. This leads to the notion of J-balanced metrics. We prove that the existence of J-balanced metrics has a purely algebro-geometric characterization in terms of Chow stability, complementing the result of Dervan-Keller. We also obtain various criteria that imply uniform J-stability and uniform K-stability, strengthening the results of Dervan-Keller. Eventually, we discuss the case of Kahler classes that may not be integral over a compact manifold.
引用
收藏
页码：391 / 412
页数：22
相关论文
共 44 条
[1]  
[Anonymous], 2014, GRADUATE STUDIES MAT
[2]  
[Anonymous], 2010, Adv. Lect. Math. (ALM)
[3]  
[Anonymous], 2000, Lectures in Mathematics ETH Zurich
[4]  
[Anonymous], 1987, DMV SEMINAR
[5]   Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability [J].
Apostolov, Vestislav ;
Calderbank, DavidM. J. ;
Gauduchon, Paul ;
Tonnesen-Friedman, Christina W. .
INVENTIONES MATHEMATICAE, 2008, 173 (03) :547-601
[6]  
BERMAN R. J., 2016, MATHDG160203114 ARXI
[7]  
BERMAN R. J., 2015, MATHDG150904561 ARXI
[8]  
BOUCKSOM S., 2015, MATHAG150406568 ARXI
[9]  
CHEN X.X., 2015, MATHDG150606423 ARXI
[10]  
Chen XX, 2000, INT MATH RES NOTICES, V2000, P607
12345