Lelong numbers of bidegree (1, 1) currents on multiprojective spaces

Let T be a positive closed current of bidegree (1, 1) on a multiprojective space X=Pn1×⋯×Pnk. For certain values of α, which depend on the cohomology class of T, we show that the set of points of X where the Lelong numbers of T exceed α have certain geometric properties. We also describe the currents T that have the largest possible Lelong number in a given cohomology class, and the set of points where this number is assumed.