Lelong numbers of currents of full mass intersection

TL;DR

This paper investigates the behavior of Lelong numbers of currents with full mass intersection on compact Kähler manifolds, introducing a new product concept for pseudoeffective classes to analyze their pluripolar parts.

Contribution

It presents a novel approach to understanding Lelong numbers by defining a new product of pseudoeffective classes that accounts for pluripolar contributions.

Findings

Extended results on Lelong numbers in mixed intersection settings

Introduced a new product capturing pluripolar parts of intersections

Connected to recent work by Darvas-Di Nezza-Lu

Abstract

We study Lelong numbers of currents of full mass intersection on a compact Kaehler manifold in a mixed setting. Our main theorems cover some recent results due to Darvas-Di Nezza-Lu. One of the key ingredients in our approach is a new notion of products of pseudoeffective classes which captures some "pluripolar part" of the "total intersection" of given pseudoeffective classes.