L2 Extensions with Singular Metrics on Kahler Manifolds

被引：0
作者：
Zhou, Xiangyu [1 ,2 ]
Zhu, Langfeng [3 ]
机构：
[1] Chinese Acad Sci, Inst Math, AMSS, Beijing 100190, Peoples R China
[2] Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2021年 / 41卷 / 06期
基金：
中国国家自然科学基金;
关键词：
singular metric; optimal L-2 extension theorem; strong openness of multiplier ideal sheaf; generalized Siu's lemma; weakly pseudoconvex Kahler manifold; MULTIPLIER IDEAL SHEAVES; OPTIMAL CONSTANT; THEOREM; REGULARIZATION; INJECTIVITY; CONJECTURE; OPENNESS; BUNDLES;
D O I：
10.1007/s10473-021-0614-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we give a survey of our recent results on extension theorems on Kahler manifolds for holomorphic sections or cohomology classes of (pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics, and also discuss their applications and the ideas contained in the proofs.
引用
收藏
页码：2021 / 2038
页数：18
相关论文
共 45 条
[1]  
BERNDTSSON B, ARXIV08043884
[2]   The Openness Conjecture and Complex Brunn-Minkowski Inequalities [J].
Berndtsson, Bo .
COMPLEX GEOMETRY AND DYNAMICS, 2015, :29-44
[3]   A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kahler geometry [J].
Berndtsson, Bo .
INVENTIONES MATHEMATICAE, 2015, 200 (01) :149-200
[4]   Curvature of vector bundles associated to holomorphic fibrations [J].
Berndtsson, Bo .
ANNALS OF MATHEMATICS, 2009, 169 (02) :531-560
[5]   BERGMAN KERNELS AND THE PSEUDOEFFECTIVITY OF RELATIVE CANONICAL BUNDLES [J].
Berndtsson, Bo ;
Paun, Mihai .
DUKE MATHEMATICAL JOURNAL, 2008, 145 (02) :341-378
[6]   Ohsawa-Takegoshi Extension Theorem for Compact Kahler Manifolds and Applications [J].
Cao, Junyan .
COMPLEX AND SYMPLECTIC GEOMETRY, 2017, 21 :19-38
[7]   A general extension theorem for cohomology classes on non reduced analytic subspaces [J].
Cao, JunYan ;
Demailly, Jean-Pierre ;
Matsumura, Shin-ichi .
SCIENCE CHINA-MATHEMATICS, 2017, 60 (06) :949-962
[8]  
Demailly J.-P., 2012, SURV MOD MATH, V1
[9]  
Demailly J.-P., 2016, LEGACY BERNHARD RIEM, V35, P191
[10]   SINGULAR HERMITIAN METRICS ON POSITIVE LINE BUNDLES [J].
DEMAILLY, JP .
LECTURE NOTES IN MATHEMATICS, 1992, 1507 :87-104
12345