Entire pluricomplex Green functions and Lelong numbers of projective currents
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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 $\alpha \geq 2/3$, and $|V_\alpha (T)\setminus L|\leq 1$ for some complex line $L$ if $\alpha \geq 1/2$. We also prove that in dimension 2 and if $\alpha \geq 2/5$, then $|V_\alpha (T)\setminus C|\leq 1$ for some conic $C$.References
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Additional Information
- Dan Coman
- Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244-1150
- MR Author ID: 325057
- Email: dcoman@syr.edu
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1927-1935
- MSC (2000): Primary 32U25, 32U35; Secondary 32U05, 32U40
- DOI: https://doi.org/10.1090/S0002-9939-05-08193-1
- MathSciNet review: 2215761