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.

中文翻译：

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复曲面多次谐波函数跳跃数的簇点

我们表明\(\mathbf {C}^n\) 中复曲面多次谐波函数的跳跃数的簇点集对于每个\(n \ge 1\)都是离散的。我们还给出了这些聚类点集的精确表征。这些将 D. Kim 和 H. Seo 的最新结果从\(n=2\)推广到任意维度。我们的方法是分析与复曲面多次谐波函数相关的牛顿凸体的渐近行为。