Entire pluricomplex Green functions and Lelong numbers of projective currents

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 $\alpha\geq2/3$, and $\vert V_\alpha(T)\setminus L\vert\leq1$ for some complex line $L$ if $\alpha\geq1/2$. We also prove that in dimension 2 and if $\alpha\geq2/5$, then $\vert V_\alpha(T)\setminus C\vert\leq1$ for some conic $C$.