Minimal model theory for relatively trivial log canonical pairs  [ La théorie des modèles minimaux pour des paires log-canoniques relativement triviaux ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2069-2107.

Nous étudions des paires log-canoniques relatives telles que des diviseurs log-canoniques sont relativement triviaux. Nous fixons une telle paire (X,Δ)/Z et montrons la théorie des modèles minimaux pour la paire (X,Δ), assumant la théorie des modèles minimaux pour toute paire Kawamata log-terminale telle que la dimension de cette paire n’est pas aussi grande que dimZ. Nous montrons aussi la finitude de l’anneau log-canonique de toute paire log-canonique telle que la dimension de cette paire est cinq et cette paire n’est pas de type log-général.

We study relative log canonical pairs with relatively trivial log canonical divisors. We fix such a pair (X,Δ)/Z and establish the minimal model theory for the pair (X,Δ) assuming the minimal model theory for all Kawamata log terminal pairs whose dimension is not greater than dimZ. We also show the finite generation of log canonical rings for log canonical pairs of dimension five which are not of log general type.

Reçu le : 2016-09-14
Révisé le : 2017-09-19
Accepté le : 2017-11-06
Publié le : 2018-11-22
DOI : https://doi.org/10.5802/aif.3203
Classification : 14E30
Mots clés : un bon modèle minimal, une fibration de Mori, une paire log-canonique, un diviseur log-canonique relativement trivial
@article{AIF_2018__68_5_2069_0,
     author = {Hashizume, Kenta},
     title = {Minimal model theory for relatively trivial log canonical pairs},
     journal = {Annales de l'Institut Fourier},
     pages = {2069--2107},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     doi = {10.5802/aif.3203},
     language = {en},
     url = {archive.numdam.org/item/AIF_2018__68_5_2069_0/}
}
Hashizume, Kenta. Minimal model theory for relatively trivial log canonical pairs. Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 2069-2107. doi : 10.5802/aif.3203. http://archive.numdam.org/item/AIF_2018__68_5_2069_0/

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