no. 5
Minimal model theory for relatively trivial log canonical pairs
[La théorie des modèles minimaux pour des paires log-canoniques relativement triviaux]
Hashizume, Kenta1
1 Department of Mathematics Graduate School of Science Kyoto University Kyoto 606-8502, Japan
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 :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3203
Classification : 14E30
Keywords: good minimal model, Mori fiber space, log canonical pair, relatively trivial log canonical divisor
Mot clés : un bon modèle minimal, une fibration de Mori, une paire log-canonique, un diviseur log-canonique relativement trivial

Hashizume, Kenta 1

1 Department of Mathematics Graduate School of Science Kyoto University Kyoto 606-8502, Japan
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@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{\textquoteright}institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     doi = {10.5802/aif.3203},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3203/}
}
TY  - JOUR
AU  - Hashizume, Kenta
TI  - Minimal model theory for relatively trivial log canonical pairs
JO  - Annales de l'Institut Fourier
PY  - 2018
SP  - 2069
EP  - 2107
VL  - 68
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.3203/
DO  - 10.5802/aif.3203
LA  - en
ID  - AIF_2018__68_5_2069_0
ER  - 
%0 Journal Article
%A Hashizume, Kenta
%T Minimal model theory for relatively trivial log canonical pairs
%J Annales de l'Institut Fourier
%D 2018
%P 2069-2107
%V 68
%N 5
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.3203/
%R 10.5802/aif.3203
%G en
%F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.3203/

[1] Abramovich, Dan; Karu, Kalle Weak semistable reduction in characteristic 0, Invent. Math., Volume 139 (2000) no. 2, pp. 241-273 | Zbl

[2] Ambro, Florin The moduli b-divisor of an lc-trivial fibration, Compos. Math., Volume 141 (2005) no. 2, pp. 385-403 | Zbl

[3] Birkar, Caucher On existence of log minimal models II, J. Reine Angew. Math., Volume 658 (2011), pp. 99-113 | Zbl

[4] Birkar, Caucher Existence of log canonical flips and a special LMMP, Publ. Math., Inst. Hautes Étud. Sci., Volume 115 (2012), pp. 325-368 | Zbl

[5] Birkar, Caucher; Cascini, Paolo; Hacon, Christopher D.; McKernan, James Existence of minimal models for varieties of log general type, J. Am. Math. Soc., Volume 23 (2010) no. 2, pp. 405-468 | Zbl

[6] Birkar, Caucher; Hu, Zhengyu Log canonical pairs with good augmented base loci, Compos. Math., Volume 150 (2014) no. 4, pp. 579-592 | Zbl

[7] Demailly, Jean-Pierre; Hacon, Christopher D.; Păun, Mihai Extension theorems, non-vanishing and the existence of good minimal models, Acta Math., Volume 210 (2013) no. 2, pp. 203-259 | Zbl

[8] Fujino, Osamu Special termination and reduction to pl flips, Flips for 3-folds and 4-folds (Oxford Lecture Series in Mathematics and its Applications), Volume 35, Oxford University Press, 2007, pp. 63-75 | Zbl

[9] Fujino, Osamu Finite generation of the log canonical ring in dimension four, Kyoto J. Math., Volume 50 (2010) no. 4, pp. 671-684 | Zbl

[10] Fujino, Osamu Fundamental theorems for the log minimal model program, Publ. Res. Inst. Math. Sci., Volume 47 (2011) no. 3, pp. 727-789 | Zbl

[11] Fujino, Osamu Some remarks on the minimal model program for log canonical pairs, J. Math. Sci., Tokyo, Volume 22 (2015) no. 1, pp. 149-192 | Zbl

[12] Fujino, Osamu Foundations of the minimal model program, MSJ Memoirs, 35, Mathematical Society of Japan, 2017, xv+289 pages | Zbl

[13] Fujino, Osamu; Gongyo, Yoshinori On canonical bundle formulas and subadjunctions, Mich. Math. J., Volume 61 (2012) no. 2, pp. 255-264 | Zbl

[14] Fujino, Osamu; Gongyo, Yoshinori Log pluricanonical representations and the abundance conjecture, Compos. Math., Volume 150 (2014) no. 4, pp. 593-620 | Zbl

[15] Fujino, Osamu; Gongyo, Yoshinori On the moduli b-divisors of lc-trivial fibrations, Ann. Inst. Fourier, Volume 64 (2014) no. 4, pp. 1721-1735 | Zbl

[16] Fujino, Osamu; Gongyo, Yoshinori On log canonical rings, Higher dimensional algebraic geometry (Advanced Studies in Pure Mathematics), Volume 74, Mathematical Society of Japan, 2017, pp. 159-169 | Zbl

[17] Fujino, Osamu; Mori, Shigefumi A canonical bundle formula, J. Differ. Geom., Volume 56 (2000) no. 1, pp. 167-188 | Zbl

[18] Gongyo, Yoshinori Remarks on the non-vanishing conjecture, Algebraic geometry in east Asia—Taipei 2011 (Advanced Studies in Pure Mathematics), Volume 65, Mathematical Society of Japan, 2015, pp. 107-116 | Zbl

[19] Gongyo, Yoshinori; Lehmann, Brian Reduction maps and minimal model theory, Compos. Math., Volume 149 (2013) no. 2, pp. 295-308 | Zbl

[20] Hacon, Christopher D.; McKernan, James; Xu, Chenyang ACC for log canonical thresholds, Ann. Math., Volume 180 (2014) no. 2, pp. 523-571 | Zbl

[21] Hacon, Christopher D.; Xu, Chenyang Existence of log canonical closures, Invent. Math., Volume 192 (2013) no. 1, pp. 161-195 | Zbl

[22] Hashizume, Kenta Remarks on the abundance conjecture, Proc. Japan Acad. Ser. A Math. Sci., Volume 92 (2016) no. 9, pp. 101-106 | Zbl

[23] Kawamata, Yujiro Variation of mixed Hodge structures and the positivity for algebraic fiber spaces, Algebraic geometry in east Asia—Taipei 2011 (Advanced Studies in Pure Mathematics), Volume 65, Mathematical Society of Japan, 2015, pp. 27-57 | Zbl

[24] Kollár, János; Kovács, Sándor J. Log canonical singularities are Du Bois, J. Am. Math. Soc., Volume 23 (2010) no. 3, pp. 791-813 | Zbl

[25] Kollár, János; Mori, Shigefumi Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, 1998, viii+254 pages | Zbl

[26] Lai, Ching-Jui Varieties fibered by good minimal models, Math. Ann., Volume 350 (2011) no. 3, pp. 533-547 | Zbl

[27] Nakayama, Noboru Zariski-decomposition and abundance, MSJ Memoirs, 14, Mathematical Society of Japan, 2004, xiv+277 pages | Zbl

Cité par Sources :