Pure and Applied Mathematics Quarterly

Volume 14 (2018)

Number 3-4

Volume of perturbations of pseudoeffective classes

Pages: 607 – 616

DOI: https://dx.doi.org/10.4310/PAMQ.2018.v14.n3.a9


Nicholas McCleerey (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)


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.

The author was partially supported by NSF RTG grant DMS-1502632.

Received 24 May 2019

Accepted 24 June 2019

Published 5 November 2019