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Cluster Points of Jumping Numbers of Toric Plurisubharmonic Functions

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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.

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Notes

  1. The one in [3] is given in terms of a graded system of ideals, which can be converted to a psh function as discussed in [8].

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Acknowledgements

The author would like to thank Dano Kim for his helpful and valuable comments. He also wishes to thank the referee for careful reading and useful comments. This research was supported by BK21 PLUS SNU Mathematical Sciences Division and by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2020R1A6A3A01099387).

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  1. Research Institute of Mathematics, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea

    Hoseob Seo

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  1. Hoseob Seo
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Correspondence to Hoseob Seo.

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Seo, H. Cluster Points of Jumping Numbers of Toric Plurisubharmonic Functions. J Geom Anal 31, 12624–12632 (2021). https://doi.org/10.1007/s12220-021-00730-0

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