论文标题
关于乘数的注释，在具有奇异性的复杂空间上
A note on multiplier ideal sheaves on complex spaces with singularities
论文作者
论文摘要
本注释的目的是提出有关乘数在复杂空间和plurisubharmonic函数的奇异性上的乘数理想带的最新结果。首先，我们通过Ohsawa的扩展度量在复杂空间（\ emph {not}）上引入乘数理想带，作为一种特殊情况，事实证明，它是代数微观设置中所谓的Mather-Jacobian乘数理想。作为应用程序，我们获得了（代数）伴随理想带的合理概括为分析设置，并从\ emph {singular} hypersurfaces上建立一些扩展定理。依靠我们的乘数和伴随理想，我们还为与Plurisubharmonic功能相关的几个重要类别的奇异性提供了特征。 此外，我们还研究了plurisubharmonic函数对数规范轨迹的奇异性的局部结构。尤其是在三维情况下，我们表明，对于具有对数规范奇点的任何多元式函数，其相关的乘数理想子处理是弱正常的，通过它，我们将其完整地分类具有对数典型奇异性的乘数理想子计算。
The goal of this note is to present some recent results of our research concerning multiplier ideal sheaves on complex spaces and singularities of plurisubharmonic functions. We firstly introduce multiplier ideal sheaves on complex spaces (\emph{not} necessarily normal) via Ohsawa's extension measure, as a special case of which, it turns out to be the so-called Mather-Jacobian multiplier ideals in the algebro-geometric setting. As applications, we obtain a reasonable generalization of (algebraic) adjoint ideal sheaves to the analytic setting and establish some extension theorems on Kähler manifolds from \emph{singular} hypersurfaces. Relying on our multiplier and adjoint ideals, we also give characterizations for several important classes of singularities of pairs associated to plurisubharmonic functions. Moreover, we also investigate the local structure of singularities of log canonical locus of plurisubharmonic functions. Especially, in the three-dimensional case, we show that for any plurisubharmonic function with log canonical singularities, its associated multiplier ideal subscheme is weakly normal, by which we give a complete classification of multiplier ideal subschemes with log canonical singularities.
