[Le théorème de Nakamaye dans les paires log-canoniques]
On propose une généralisation de la description de Nakamaye, par le biais de la théorie d’intersection, du lieu de base augmenté d’un diviseur grand et nef sur une paire normale avec singularités log-canoniques ou, plus généralement, sur une variété avec lieu non-lc de dimension . On propose aussi une généralisation de la description de Ein-Lazarsfeld-Mustaţă-Nakamaye-Popa, en termes de valuations, des sous-variétés du lieu de base restreint d’un diviseur grand sur une paire normale avec singularités klt.
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 . We also generalize Ein-Lazarsfeld-Mustaţă-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: Base loci, log-canonical singularities, non-lc ideal
Mot clés : lieux de base, singularités log-canoniques, idéaux non-lc
@article{AIF_2014__64_6_2283_0,
author = {Cacciola, Salvatore and Lopez, Angelo Felice},
title = {Nakamaye{\textquoteright}s theorem on log canonical pairs},
journal = {Annales de l'Institut Fourier},
pages = {2283--2298},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {64},
number = {6},
year = {2014},
doi = {10.5802/aif.2913},
zbl = {06387340},
mrnumber = {3331167},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2913/}
}
TY - JOUR AU - Cacciola, Salvatore AU - Lopez, Angelo Felice TI - Nakamaye’s theorem on log canonical pairs JO - Annales de l'Institut Fourier PY - 2014 SP - 2283 EP - 2298 VL - 64 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2913/ DO - 10.5802/aif.2913 LA - en ID - AIF_2014__64_6_2283_0 ER -
%0 Journal Article %A Cacciola, Salvatore %A Lopez, Angelo Felice %T Nakamaye’s theorem on log canonical pairs %J Annales de l'Institut Fourier %D 2014 %P 2283-2298 %V 64 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2913/ %R 10.5802/aif.2913 %G en %F AIF_2014__64_6_2283_0
Cacciola, Salvatore; Lopez, Angelo Felice. Nakamaye’s theorem on log canonical pairs. Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2283-2298. doi : 10.5802/aif.2913. http://www.numdam.org/articles/10.5802/aif.2913/
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