Geometric properties of upper level sets of Lelong numbers on projective spaces

Abstract

Let \(T\) be a positive closed current of unit mass on the complex projective space \(\mathbb P^n\). For certain values \(\alpha <1\), we prove geometric properties of the set of points in \(\mathbb P^n\) where the Lelong number of \(T\) exceeds \(\alpha \). We also consider the case of positive closed currents of bidimension (1,1) on multiprojective spaces.