A Kahlerness criterion for real (1,1)-classes on projective manifolds through extendibility of singular potentials  

作　　者：Xiankui Meng Zhiwei Wang 

机构地区：[1]School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China [2]Laboratory of Mathematics and Complex Systems(Ministry of Education),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China

出　　处：《Science China Mathematics》2022年第9期1795-1802,共8页中国科学：数学（英文版）

基　　金：supported by the National Key Research and Development Program of China(Grant No.2021YFA1002600);supported by National Natural Science Foundation of China(Grant No.11901046);supported by the Beijing Natural Science Foundation(Grant Nos.1202012 and Z190003);National Natural Science Foundation of China(Grant No.12071035)。

摘　　要：Let X be a projective manifold and let{θ}∈H 1,1(X,R)be a nonzero pseudo-effective(transcendental)class,where θ is a smooth closed real(1,1)-form.We prove that if for any one-dimensional complex submanifold C⊂X and φ∈SPsh(C,θ|C)with a single analytic singularity at some point p∈C,there exists a function φ∈Psh(X,θ)such that φ|C=φ and φ is continuous at points of C∖{p},then{θ}is a Kahler class.

关 键 词：transcendental class quasi-psh function Kahler class 

分 类 号：O174[理学—数学]