TY - JOUR

T1 - Entire pluricomplex green functions and lelong numbers of projective currents

AU - Coman, Dan

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2006/7

Y1 - 2006/7

N2 - 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.

AB - 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.

KW - Lelong numbers

KW - Pluricomplex Green functions

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U2 - 10.1090/S0002-9939-05-08193-1

DO - 10.1090/S0002-9939-05-08193-1

M3 - Article

AN - SCOPUS:33745945453

VL - 134

SP - 1927

EP - 1935

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -