The Augmented Base Locus in Positive Characteristic

Paolo Cascini, James McKernan, Mircea Mustaţǎ
2013 Proceedings of the Edinburgh Mathematical Society  
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 L| V is not big. For a smooth variety in characteristic zero, this was proved by Nakamaye using vanishing theorems. ) = 0. When X is a smooth projective variety in characteristic zero, the above theorem was proved in [5], making use of the Kawamata-Viehweg vanishing theorem. It is an interesting
more » ... n interesting question whether the result holds in characteristic zero when the variety is singular. Key words and phrases. Stable base locus, augmented base locus, big and nef line bundle.
doi:10.1017/s0013091513000916 fatcat:52ovnvajofeg7nzpmnsagphvmm