English

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.

Keywords

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

R2 v1 2026-06-21T19:35:46.556Z