Loss of mass of non-pluripolar products

TL;DR

This paper provides a quantitative analysis of the mass loss in non-pluripolar products of positive currents on compact Kähler manifolds, extending existing theories with new inequalities and concepts.

Contribution

It introduces a quantitative version of mass loss for non-pluripolar products, generalizes Demailly's comparison to density currents, and develops the notion of relative non-pluripolar products.

Findings

Quantitative bounds on mass loss in non-pluripolar products

Generalization of Demailly's comparison to density currents

Reversed Alexandrov-Fenchel inequality for these currents

Abstract

It is a well-known fact that the non-pluripolar self-products of a closed positive (1,1)-current in a big nef cohomology class on a compact Kahler manifold are not of full mass in the presence of positive Lelong numbers of the current in consideration. In this paper, we give a quantitative version of the last property. Our proof involves a generalization of Demailly's comparison of Lelong numbers to the setting of density currents, a reversed Alexandrov-Fenchel inequality, and the notion of relative non-pluripolar products.