Lelong numbers of bidegree (1, 1) currents on multiprojective spaces

Abstract

Let T be a positive closed current of bidegree (1, 1) on a multiprojective space \(X={\mathbb P}^{n_1}\times \cdots \times {{\mathbb {P}}}^{n_k}\). For certain values of \(\alpha \), which depend on the cohomology class of T, we show that the set of points of X where the Lelong numbers of T exceed \(\alpha \) have certain geometric properties. We also describe the currents T that have the largest possible Lelong number in a given cohomology class, and the set of points where this number is assumed.

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Correspondence to James Heffers.

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D. Coman is partially supported by the NSF Grant DMS-1700011.

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Coman, D., Heffers, J. Lelong numbers of bidegree (1, 1) currents on multiprojective spaces. Math. Z. 295, 1569–1582 (2020). https://doi.org/10.1007/s00209-019-02427-1

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Keywords

  • Positive closed currents
  • Plurisubharmonic functions
  • Lelong numbers

Mathematics Subject Classification

  • Primary 32U25
  • Secondary 32U05
  • 32U40