Cluster points of jumping numbers of toric plurisubharmonic functions

TL;DR

This paper proves that the cluster points of jumping numbers for toric plurisubharmonic functions are discrete and characterizes them precisely, extending previous results from two dimensions to all dimensions using convex geometric analysis.

Contribution

It generalizes the discreteness and characterization of cluster points of jumping numbers from 2D to arbitrary dimensions for toric plurisubharmonic functions.

Findings

Cluster points of jumping numbers are discrete in all dimensions.

A precise characterization of these cluster points is provided.

The method involves analyzing asymptotic behaviors of Newton convex bodies.

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.