Nadel-type multiplier ideal sheaves on complex spaces with singularities  

作　　者：Zhenqian Li 

机构地区：[1]School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China [2]Siwuge Technology Co.Ltd.,Chengdu 610093,China

出　　处：《Science China Mathematics》2024年第5期951-974,共24页中国科学（数学）（英文版）

摘　　要：In this article,we introduce multiplier ideal sheaves on complex spaces with singularities(not necessarily normal)via Ohsawa’s extension measure,as a special case of which,it turns out to be the socalled Mather-Jacobian multiplier ideals in the algebro-geometric setting.Inspired by Nadel’s coherence and Guan-Zhou’s strong openness properties of the multiplier ideal sheaves,we discuss similar properties for the generalized multiplier ideal sheaves.As applications,we obtain a reasonable generalization of(algebraic)adjoint ideal sheaves to the analytic setting and establish some extension theorems on K?hler manifolds from singular hypersurfaces.Relying on our multiplier and adjoint ideals,we also give characterizations for several important classes of singularities of pairs associated with plurisubharmonic functions.

关 键 词：multiplier ideal sheaves plurisubharmonic functions Ohsawa-Takegoshi Luextension theorem rational singularities 

分 类 号：O174.5[理学—数学]