Nakamaye's theorem on log canonical pairs
Algebraic Geometry
2014-12-24 v4
Abstract
We generalize Nakamaye's description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension at most 1. We also generalize Ein-Lazarsfeld-Mustata-Nakamaye-Popa's description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.
Keywords
Cite
@article{arxiv.1303.7156,
title = {Nakamaye's theorem on log canonical pairs},
author = {Salvatore Cacciola and Angelo Felice Lopez},
journal= {arXiv preprint arXiv:1303.7156},
year = {2014}
}
Comments
v2: We removed, in the introduction, the phrase about Choi's papers, as he uses Nakamaye's theorem in the semiample case. Updated references. v3: added reference to Ambro's "Quasi-log varieties". v4: improved exposition in sections 1, 2 and 4; slightly corrected the statement of Lemma 3.1