Upper level sets of Lelong numbers on P2 and cubic curves

Let T be a positive closed current of bidimension (1, 1) with unit mass on P 2 and V α ( T ) be the upper level sets of Lelong numbers ν ( T , x ) of T . For any α ≥ 1 3 , we show that | V α ( T ) \ C | ≤ 2 for some cubic curve C .

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Bibliographic Details
Published in:Mathematische Zeitschrift 2022, Vol.300 (3), p.2917-2930
Main Authors: Kisisel, Ali Ulas Ozgur, Yazici, Ozcan
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Description
Summary:Let T be a positive closed current of bidimension (1, 1) with unit mass on P 2 and V α ( T ) be the upper level sets of Lelong numbers ν ( T , x ) of T . For any α ≥ 1 3 , we show that | V α ( T ) \ C | ≤ 2 for some cubic curve C .
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-021-02907-3