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Entire pluricomplex Green functions and Lelong numbers of projective currents

Author: Dan Coman
Journal: Proc. Amer. Math. Soc. 134 (2006), 1927-1935
MSC (2000): Primary 32U25, 32U35; Secondary 32U05, 32U40
Published electronically: December 19, 2005
MathSciNet review: 2215761
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Abstract: Let $ T$ be a positive closed current of bidimension (1,1) and unit mass on the complex projective space $ {\mathbb{P}}^n$. We prove that the set $ V_\alpha(T)$ of points where $ T$ has Lelong number larger than $ \alpha$ is contained in a complex line if $ \alpha\geq2/3$, and $ \vert V_\alpha(T)\setminus L\vert\leq1$ for some complex line $ L$ if $ \alpha\geq1/2$. We also prove that in dimension 2 and if $ \alpha\geq2/5$, then $ \vert V_\alpha(T)\setminus C\vert\leq1$ for some conic $ C$.

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Additional Information

Dan Coman
Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244-1150

Keywords: Pluricomplex Green functions, Lelong numbers
Received by editor(s): September 9, 2004
Received by editor(s) in revised form: February 1, 2005
Published electronically: December 19, 2005
Additional Notes: The author was supported by NSF grant DMS 0140627
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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