Pathologies of the volume function -- John Lesieutre, July 8, 2020.

Abstract: The "volume" of a line bundle L on a projective variety is a measure of the growth rate of the number of sections of its tensor powers L^{\otimes m}. I will describe two examples in which the behavior of this function near the pseudoeffective boundary has unexpectedly complicated behavior, and discuss some implications for attempts to define a numerical analog of the Iitaka dimension.