The augmented base locus in positive characteristic

Abstract

Let L be a nef line bundle on a projective scheme X in positive characteristic. We prove that the augmented base locus of L is equal to the union of the irreducible closed subsets V of X such that the restriction of L to V is not big. For a smooth variety in characteristic zero, this was proved by Nakamaye using vanishing theorems.

9 pages; v.2: minor corrections, to appear in Proceedings of the Edinburgh Mathematical Society, volume dedicated to V.V. Shokurov