Asian Journal of Mathematics

Volume 24 (2020)

Number 4

Cluster points of jumping coefficients and equisingularities of plurisubharmonic functions

Pages: 611 – 620

DOI: https://dx.doi.org/10.4310/AJM.2020.v24.n4.a4

Authors

Qi’an Guan (School of Mathematical Sciences, and Beijing International Center for Mathematical Research, Peking University, Beijing, China)

Zhenqian Li (Institute for Mathematical Sciences, Renmin University of China, Beijing, China)

Abstract

In this article, we will construct a plurisubharmonic function whose jumping coefficients have a cluster point. We also give a class of plurisubharmonic functions which cannot be “strongly equisingular” to any plurisubharmonic function with generalized analytic singularities and present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.

Keywords

plurisubharmonic function, multiplier ideal sheaf, lelong number, equisingularity

2010 Mathematics Subject Classification

32C35, 32U05, 32U25

Full Text (PDF format)

Both authors would like to sincerely thank their supervisor, Professor Xiangyu Zhou, for valuable discussions and useful comments. They also thank the referee for his/her careful reading and crucial suggestions. The second author is also grateful to the Beijing International Center for Mathematical Research for its excellent working conditions.

The first author was supported by NSFC-11825101, NSFC-11522101 and NSFC-11431013.

Received 12 May 2017

Accepted 15 November 2019

Published 18 February 2021