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Upper level sets of Lelong numbers on \(\mathbb P^2\) and cubic curves

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Let T be a positive closed current of bidimension (1, 1) with unit mass on \(\mathbb P^2\) and \(V_{\alpha }(T)\) be the upper level sets of Lelong numbers \(\nu (T,x)\) of T. For any \(\alpha \ge \frac{1}{3}\), we show that \(|V_{\alpha }(T){\setminus } C|\le 2\) for some cubic curve C.

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We would like to thank to the referee for his/her careful reading and suggestions. The second author is supported by TÜBİTAK 3501 Proj. No. 120F084 and TÜBİTAK 2518 Proj. No. 119N642.

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Correspondence to Ozcan Yazici.

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Kisisel, A.U.O., Yazici, O. Upper level sets of Lelong numbers on \(\mathbb P^2\) and cubic curves. Math. Z. 300, 2917–2930 (2022).

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