Density and intersection of (1,1)-currents

TL;DR

This paper investigates the properties of density currents linked to positive closed (1,1)-currents, establishing their uniqueness and relation to classical wedge products, with applications to non-pluripolar and Andersson-Wulcan products.

Contribution

It proves the uniqueness of density currents and explores their relation to classical wedge products and other products in complex geometry.

Findings

Density currents are unique in certain classical cases.

Density currents coincide with wedge products when potentials are bounded.

Explicit computations of density in cases where wedge products are undefined.

Abstract

We study density currents associated with a collection of positive closed (1,1)-currents. We prove that the density current is unique and determined by the usual wedge product in some classical situations including the case where the currents have bounded potentials. As an application, we compare density currents with the non-pluripolar product and the Andersson-Wulcan product. We also analyse some situations where the wedge product is not well-defined but the density can be explicitly computed.