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Jumping numbers of analytic multiplier ideals (with an appendix by Sébastien Boucksom)

Volume 124 / 2020

Dano Kim, Hoseob Seo Annales Polonici Mathematici 124 (2020), 257-280 MSC: Primary 32U05; Secondary 14F18, 32U25. DOI: 10.4064/ap190529-19-12 Published online: 19 March 2020

Abstract

We extend the study of jumping numbers of multiplier ideals due to Ein–Lazarsfeld–Smith–Varolin from the algebraic case to the case of general plurisubharmonic functions. While many properties established by Ein–Lazarsfeld–Smith–Varolin are shown to generalize to the plurisubharmonic case, important properties such as periodicity and discreteness do not hold any more. Previously only two particular examples with a cluster point (i.e. failure of discreteness) of jumping numbers were known, due to Guan–Li and to Ein–Lazarsfeld–Smith–Varolin. We generalize them to all toric plurisubharmonic functions in dimension 2 by characterizing precisely when cluster points of jumping numbers exist and by computing all those cluster points. This characterization suggests that clustering of jumping numbers is a rather frequent phenomenon. In particular, we obtain uncountably many new such examples.

Authors

  • Dano KimDepartment of Mathematical Sciences &
    Research Institute of Mathematics
    Seoul National University
    1 Gwanak-ro, Gwanak-gu
    Seoul 08826, Republic of Korea
    e-mail
  • Hoseob SeoDepartment of Mathematical Sciences
    Seoul National University
    1 Gwanak-ro, Gwanak-gu
    Seoul 08826, Republic of Korea
    e-mail

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