On equisingular approximation of plurisubharmonic functions

TL;DR

This paper investigates conditions under which plurisubharmonic functions can be approximated by functions with analytic singularities, focusing on toric functions and extending recent results to broader classes.

Contribution

It provides a criterion for approximating toric plurisubharmonic functions with analytic singularities, generalizing previous work by Guan.

Findings

Established a criterion for toric functions

Extended Guan's results to broader classes

Provided insights into equisingular approximation methods

Abstract

It is a natural question to ask which plurisubharmonic functions admit a 'nice' approximation in the sense of a decreasing equisingular approximation with analytic singularities. For arbitrary toric plurisubharmonic functions, we give a criterion for admitting a nice approximation with toric approximants. Our results are motivated by a recent result of Guan for toric plurisubharmonic functions of the diagonal type.