Stability of weighted log canonical threshold of plurisubharmonic functions

Abstract

Let φ be a plurisubharmonic function on an open subset $\Omega \subset C^n$. We know that φ has a singularity at point a if $\phi \left(a\right)=-\infty$. Two of the most important measures of singularities are the Lelong number and the log canonical threshold. In this article, we study the stability of weighted log canonical thresholds $c_{\mu }\left(\phi \right)$ with measure $\mu ={\left({\sum }_{k=1}^m\right|f_k{|}^2)}^{t}d{V}_{2n}$ for any $t\in R$. The result obtained leads to a principle for comparing Nadel's multiplier ideal sheaves.