The augmented base locus in positive characteristic
Algebraic Geometry
2012-01-20 v2
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.
Cite
@article{arxiv.1111.3236,
title = {The augmented base locus in positive characteristic},
author = {Paolo Cascini and James McKernan and Mircea Mustata},
journal= {arXiv preprint arXiv:1111.3236},
year = {2012}
}
Comments
9 pages; v.2: minor corrections, to appear in Proceedings of the Edinburgh Mathematical Society, volume dedicated to V.V. Shokurov