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

  • Dan Coman
  • James HeffersEmail author


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.


Positive closed currents Plurisubharmonic functions Lelong numbers 

Mathematics Subject Classification

Primary 32U25 Secondary 32U05 32U40 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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