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

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.

References in corpus (1)

• Quasiplurisubharmonic Green functions

Cited by in corpus (3)

• Lelong Numbers of Bidegree (1,1) Currents on Multiprojective Spaces
• Upper level sets of Lelong numbers on ${\mathbb{P}}^2$ and cubic curves
• On Lelong Numbers of Positive Closed Currents on ${\mathbb{P}}^n$