Entire pluricomplex green functions and lelong numbers of projective currents

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5 Scopus citations

Abstract

Let T be a positive closed current of bidimension (1,1) and unit mass on the complex projective space ℙ n. We prove that the set V α(T) of points where T has Lelong number larger than a is contained in a complex line if α ≥ 2/3, and |V α(T) \ L| ≤ 1 for some complex line L if α ≥ 1/2. We also prove that in dimension 2 and if α ≥ 2/5, then |V α(T) \C| ≤ 1 for some conic C.

Original languageEnglish (US)
Pages (from-to)1927-1935
Number of pages9
JournalProceedings of the American Mathematical Society
Volume134
Issue number7
DOIs
StatePublished - Jul 2006

Keywords

  • Lelong numbers
  • Pluricomplex Green functions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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