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Lelong Number and the Log Canonical Thresholds of Plurisubharmonic Functions on Analytic Subsets

Abstract

The aim of this paper is to introduce the notion of Lelong number and the log canonical thresholds of plurisubharmonic functions on analytic subsets A in an open subset Ω of \(\mathbb {C}^{n}\). Next, we establish some results about the relationship between these quantities in the relation with the analyticity of A.

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Acknowledgments

The authors would like to thank the referees very much for carefully reading the paper and for valuable remarks and suggestions which led to the improvements of the exposition of the paper. The third author would like to thank IMU for supporting his Ph.D studies at Hanoi National University of Education through the IMU Breakout Graduate Fellowship.

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Correspondence to Le Mau Hai.

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Hai, L.M., Hiep, P.H. & Tung, T. Lelong Number and the Log Canonical Thresholds of Plurisubharmonic Functions on Analytic Subsets. Acta Math Vietnam 47, 223–241 (2022). https://doi.org/10.1007/s40306-021-00465-8

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  • DOI: https://doi.org/10.1007/s40306-021-00465-8

Keywords

  • Pure k-dimensional analytic subsets
  • Irreducible analytic subset
  • Ramified coverings
  • Plurisubharmonic functions on analytic subsets
  • Lelong number
  • The log canonical thresholds

Mathematics Subject Classification (2010)

  • 32C25
  • 32C30
  • 32U25
  • 32W20