Local positivity in terms of Newton-Okounkov bodies

摘要

In recent years, the study of Newton-Okounkov bodies on normal varieties has become a central subject in the asymptotic theory of linear series, after its introduction by Lazarsfeld-Mustafg and Kaveh-Khovanskii. One reason for this is that they encode all numerical equivalence information of divisor classes (by work of Jow). At the same time, they can be seen as local positivity invariants, and Kiironya-Lozovanu have studied them in depth from this point of view.