# Volume of Perturbations of Pseudoeffective Classes

## TL;DR

This paper investigates how the volume function of pseudoeffective classes on compact Kähler manifolds behaves near the boundary of the pseudoeffective cone, providing polynomial behavior results in specific cases.

## Contribution

It offers new insights into the asymptotic behavior of the volume function near the boundary, especially for classes with numerical dimension zero.

## Key findings

- Volume function behaves polynomially near boundary for classes with numerical dimension zero
- Solved asymptotic behavior in several cases of pseudoeffective classes
- Provides a deeper understanding of the geometry of the pseudoeffective cone

## Abstract

In this short note, we consider the question of determining the asymptotics of the volume function near the boundary of the pseudoeffective cone on compact K\"ahler manifolds. We solve the question in a number of cases -- in particular, we show that the volume function behaves polynomially under small perturbations near pseudoeffective classes with numerical dimension zero.