Decreasing Equisingular Approximations with Analytic Singularities

  • Qi’an GuanEmail author


In this note, for the multiplier ideal sheaves with weights \(\log \sum _{i}|z_{i}|^{a_{i}}\), we present the sufficient and necessary condition of the existence of decreasing equisingular approximations with analytic singularities.


Multiplier ideal sheaf Plurisubharmonic function Equisingular approximation Analytic singularity 

Mathematics Subject Classification

32D15 32E10 32L10 32U05 



The author would like to thank Professor Jean-Pierre Demailly, Professor Takeo Ohsawa, and Professor Xiangyu Zhou for helpful discussions and encouragements. The author would also like to thank the hospitality of Beijing International Center for Mathematical Research. The author was supported by grants Nos. NSFC-11825101, NSFC-11522101, and NSFC-11431013.


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Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina

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