Approximation and equidistribution results for pseudo-effective line bundles

TL;DR

This paper investigates how the zero sets of sections of pseudo-effective line bundles distribute on compact Kähler manifolds, providing conditions for approximating curvature current products by analytic cycles.

Contribution

It introduces new approximation conditions for wedge products of curvature currents of pseudo-effective line bundles on Kähler manifolds.

Findings

Distribution of zero sets analyzed

Conditions for approximation of curvature currents established

Wedge products approximated by analytic cycles

Abstract

We study the distribution of the common zero sets of $m$-tuples of holomorphic sections of powers of $m$ singular Hermitian pseudo-effective line bundles on a compact K\"ahler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles can be approximated by analytic cycles.