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arXiv · 1610.05265

A Property of Upper Level Sets of Lelong Numbers of Currents on $\mathbb{P}^2$

James J. Heffers
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Abstract

Let $T$ be a positive closed current of bidimension $(1,1)$ with unit mass on the complex projective space $\mathbb P^2$. For $\alpha > 2/5$ and $\beta = (2-2\alpha)/3$ we show that if $T$ has four point with Lelong number greater than $\alpha$, the upper level set $E_{\beta}^+ (T)$ of points of $T$ with Lelong number strictly larger than $\beta$ is contained within a conic with the exception of at most one point.

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James J. Heffers. 2016-10-17. A Property of Upper Level Sets of Lelong Numbers of Currents on $\mathbb{P}^2$. https://doi.org/10.1142/s0129167x17501105

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