Pathologies of the volume function

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.

Russianalgebraic geometry

Audience: researchers in the topic

Iskovskikh seminar

Series comments: Description: Seminar