Entire pluricomplex Green functions and Lelong numbers of projective currents

2004/09/13 by Dan Coman, Coman, Dan
Mathematics · #32U35. Secondary: 32U05 #32U40 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 32U25 #math.CV #msc:32U05 #msc:32U25 #msc:32U35. #msc:32U40

paper · pdf · doi:10.48550/arxiv.math/0409210

9 pages

arxiv created 2004/09/13 · arxiv updated 2009/12/01

Abstract

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

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