The non-nef locus in positive characteristic

TL;DR

This paper extends the understanding of the non-nef locus to positive characteristic by replacing asymptotic multiplier ideals with asymptotic test ideals, supported by a uniform global generation result.

Contribution

It introduces an analogue of the non-nef locus description in positive characteristic using asymptotic test ideals instead of multiplier ideals.

Findings

Established a positive characteristic analogue of the non-nef locus description.

Proved a uniform global generation statement involving asymptotic test ideals.

Connected asymptotic test ideals with geometric properties of the non-nef locus.

Abstract

We give an analogue in positive characteristic of the description of the non-nef locus from \cite{ELMNP}. In this case, the role of the asymptotic multiplier ideals is played by the asymptotic test ideals. The key ingredient is provided by a uniform global generation statement involving twists by such ideals.