Augmented base loci and restricted volumes on normal varieties
Algebraic Geometry
2014-12-24 v2
Abstract
We extend to normal projective varieties defined over an arbitrary algebraically closed field a result of Ein, Lazarsfeld, Musta\c{t}\u{a}, Nakamaye and Popa characterizing the augmented base locus (aka non-ample locus) of a line bundle on a smooth projective complex variety as the union of subvarieties on which the restricted volume vanishes. We also give a proof of the folklore fact that the complement of the augmented base locus is the largest open subset on which the Kodaira map defined by large and divisible multiples of the line bundle is an isomorphism.
Cite
@article{arxiv.1305.4284,
title = {Augmented base loci and restricted volumes on normal varieties},
author = {Sébastien Boucksom and Salvatore Cacciola and Angelo Felice Lopez},
journal= {arXiv preprint arXiv:1305.4284},
year = {2014}
}
Comments
7 pages. v2: we made a small modification of the statement of Lemma 2.4, a few minor corrections and updated references