Decreasing equisingular approximations with analytic singularities

TL;DR

This paper establishes the necessary and sufficient conditions for the existence of decreasing equisingular approximations with analytic singularities for certain multiplier ideal sheaves, advancing understanding of their structure.

Contribution

It provides a complete characterization of when decreasing equisingular approximations with analytic singularities exist for specific multiplier ideal sheaves.

Findings

Characterization of existence conditions for approximations

Necessary and sufficient criteria established

Advances understanding of multiplier ideal sheaves with logarithmic weights

Abstract

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.