Volume of Perturbations of Pseudoeffective Classes

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 Kähler 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.

8 pages