Singularity of non-pluripolar cohomology classes

Abstract

We establish a relation between Lelong numbers and the full mass property of relative non-pluripolar products. We use this relation to prove that if the restricted volume of a big class $\alpha$ along an effective divisor $D$ is of full mass, then the Lelong numbers of the non-pluripolar class $⟨{\alpha }^{n-1}⟩$ at every point in the support of $D$ are zero. In particular, we obtain that on projective manifolds, the Lelong numbers of the non-pluripolar class $⟨{\alpha }^{n-1}⟩$ of a big class $\alpha$ are zero.

16 pages, last version, to appear in Bulletin of the London Mathematical Society