Transcendental b-divisors II -- Monotonicity theorem

TL;DR

This paper extends the intersection theory of nef b-divisors, introduces a restricted volume concept, and proves a monotonicity theorem leading to new volume inequalities for currents and cohomology classes.

Contribution

It develops a general intersection theory for nef b-divisors, including a new notion of restricted volume and a monotonicity theorem.

Findings

Proved a quantitative monotonicity of the intersection product.

Established new volume inequalities for currents.

Extended movable intersection theory to nef b-divisors.

Abstract

In this paper, we develop the general intersection theory of nef b-divisors, extending the movable intersection theory. We define a notion of restricted volume of b-divisors and prove a quantitative version of the monotonicity of the intersection product. As a consequence, we prove a number of new volume inequalities of currents and cohomology classes.