Entire pluricomplex Green functions and Lelong numbers of projective currents

Let TT be a positive closed current of bidimension (1,1) and unit mass on the complex projective space Pn{\mathbb P}^n. We prove that the set Vα(T)V_\alpha (T) of points where TT has Lelong number larger than α\alpha is contained in a complex line if α≥2/3\alpha \geq 2/3, and |Vα(T)∖L|≤1|V_\alpha (T...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2006-07, Vol.134 (7), p.1927-1935
Main Author: Coman, Dan
Format: Article
Language:English
Subjects:
Algebra
Conic sections
Degrees of polynomials
Exact sciences and technology
Greens function
Linear polynomials
Mathematical analysis
Mathematical functions
Mathematical theorems
Mathematics
Polynomials
Quadratic polynomials
Research article
Sciences and techniques of general use
Several complex variables and analytic spaces
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Summary:Let TT be a positive closed current of bidimension (1,1) and unit mass on the complex projective space Pn{\mathbb P}^n. We prove that the set Vα(T)V_\alpha (T) of points where TT has Lelong number larger than α\alpha is contained in a complex line if α≥2/3\alpha \geq 2/3, and |Vα(T)∖L|≤1|V_\alpha (T)\setminus L|\leq 1 for some complex line LL if α≥1/2\alpha \geq 1/2. We also prove that in dimension 2 and if α≥2/5\alpha \geq 2/5, then |Vα(T)∖C|≤1|V_\alpha (T)\setminus C|\leq 1 for some conic CC.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-08193-1