Transcendental b-divisors I -- Correspondence with currents

TL;DR

This paper explores the relationship between transcendental b-divisors and currents on compact Kähler manifolds, establishing a correspondence and developing intersection theory for nef b-divisors.

Contribution

It introduces a correspondence between closed positive currents and nef b-divisors, and develops intersection theory for nef b-divisors on Kähler manifolds.

Findings

Established the correspondence between closed positive currents and nef b-divisors.

Developed intersection theory for nef b-divisors.

Answered a question of Dang--Favre regarding intersection theory.

Abstract

We study transcendental b-divisors over compact K\"ahler manifolds. We establish the correspondence between closed positive currents and nef b-divisors. As an application, we establish the intersection theory of nef b-divisors, answering a question of Dang--Favre.