Abstract
We extend to normal projective varieties defined over an arbitrary algebraically closed field a result of Ein, Lazarsfeld, Mustaţă, 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.
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We wish to thank Lorenzo Di Biagio, Gianluca Pacienza and Paolo Cascini for some helpful discussions.
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Sébastien Boucksom: Research partially supported by ANR projects MACK and POSITIVE.
Salvatore Cacciola, Angelo Felice Lopez: Research partially supported by the MIUR national project “Geometria delle varietà algebriche” PRIN 2010–2011.
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Boucksom, S., Cacciola, S. & Lopez, A.F. Augmented base loci and restricted volumes on normal varieties. Math. Z. 278, 979–985 (2014). https://doi.org/10.1007/s00209-014-1341-3
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DOI: https://doi.org/10.1007/s00209-014-1341-3