Upper level sets of Lelong numbers on ${\mathbb{P}}^2$ and cubic curves

Abstract

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 $C$.

References in corpus (1)

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