Cluster Points of Jumping Numbers of Toric Plurisubharmonic Functions

Abstract

We show that the set of cluster points of jumping numbers of a toric plurisubharmonic function in $\mathbf{C}^n$ is discrete for every $n \ge 1$. We also give a precise characterization of the set of those cluster points. These generalize a recent result of D. Kim and H. Seo from $n=2$ to arbitrary dimension. Our method is to analyze the asymptotic behaviors of Newton convex bodies associated to toric plurisubharmonic functions.