Minimal model theory for relatively trivial log canonical pairs
Annales de l'Institut Fourier, Volume 68 (2018) no. 5, p. 2069-2107
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.
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.
Received : 2016-09-15
Revised : 2017-09-20
Accepted : 2017-11-07
Published online : 2018-11-23
DOI : https://doi.org/10.5802/aif.3203
Classification:  14E30
Keywords: good minimal model, Mori fiber space, log canonical pair, relatively trivial log canonical divisor
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     pages = {2069-2107},
     doi = {10.5802/aif.3203},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2018__68_5_2069_0}
}
Minimal model theory for relatively trivial log canonical pairs. Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 2069-2107. doi : 10.5802/aif.3203. https://aif.centre-mersenne.org/item/AIF_2018__68_5_2069_0/

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