On the log canonical ring of projective plt pairs with the Kodaira dimension two
Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1775-1789.

The log canonical ring of a projective plt pair with the Kodaira dimension two is finitely generated.

L’anneau log canonique d’une paire plt projective de dimension de Kodaira deux est finement engendré.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3382
Classification: 14E30, 14N30
Keywords: log canonical ring, plt, canonical bundle formula
Mot clés : anneau log canonique, plt, formule du fibré canonique

Fujino, Osamu 1; Liu, Haidong 2

1 Department of Mathematics Graduate School of Science Osaka University Toyonaka, Osaka 560-0043 (Japan)
2 Beijing International Center for Mathematical Research Peking University Beijing 100871 (China)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{AIF_2020__70_4_1775_0,
     author = {Fujino, Osamu and Liu, Haidong},
     title = {On the log canonical ring of projective plt pairs with the {Kodaira} dimension two},
     journal = {Annales de l'Institut Fourier},
     pages = {1775--1789},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {70},
     number = {4},
     year = {2020},
     doi = {10.5802/aif.3382},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3382/}
}
TY  - JOUR
AU  - Fujino, Osamu
AU  - Liu, Haidong
TI  - On the log canonical ring of projective plt pairs with the Kodaira dimension two
JO  - Annales de l'Institut Fourier
PY  - 2020
SP  - 1775
EP  - 1789
VL  - 70
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.3382/
DO  - 10.5802/aif.3382
LA  - en
ID  - AIF_2020__70_4_1775_0
ER  - 
%0 Journal Article
%A Fujino, Osamu
%A Liu, Haidong
%T On the log canonical ring of projective plt pairs with the Kodaira dimension two
%J Annales de l'Institut Fourier
%D 2020
%P 1775-1789
%V 70
%N 4
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.3382/
%R 10.5802/aif.3382
%G en
%F AIF_2020__70_4_1775_0
Fujino, Osamu; Liu, Haidong. On the log canonical ring of projective plt pairs with the Kodaira dimension two. Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1775-1789. doi : 10.5802/aif.3382. https://aif.centre-mersenne.org/articles/10.5802/aif.3382/

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

[2] Ambro, Florin Shokurov’s boundary property, J. Differ. Geom., Volume 67 (2004) no. 2, pp. 229-255 | MR

[3] 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 | DOI | MR

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

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

[6] Fujino, Osamu Minimal model theory for log surfaces, Publ. Res. Inst. Math. Sci., Volume 48 (2012) no. 2, pp. 339-371 | DOI | MR

[7] 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 | MR | Zbl

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

[9] Fujino, Osamu Fundamental properties of basic slc-trivial fibrations I (2018) (https://arxiv.org/abs/1804.11134, to appear in Publ. Res. Inst. Math. Sci.)

[10] Fujino, Osamu; Fujisawa, Taro; Liu, Haidong Fundamental properties of basic slc-trivial fibrations II (2018) (https://arxiv.org/abs/1808.10604, to appear in Publ. Res. Inst. Math. Sci.)

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

[12] Fujino, Osamu; Gongyo, Yoshinori On log canonical rings, Higher dimensional algebraic geometry: in honour of Professor Yujiro Kawamata’s sixtieth birthday (Advanced Studies in Pure Mathematics), Volume 74, Mathematical Society of Japan, 2017, pp. 159-169 | DOI | MR

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

[14] Hashizume, Kenta Minimal model theory for relatively trivial log canonical pairs, Ann. Inst. Fourier, Volume 68 (2018) no. 5, pp. 2069-2107 | DOI | Numdam | MR

[15] Kawamata, Yujiro Log canonical models of algebraic 3-folds, Int. J. Math., Volume 3 (1992) no. 3, pp. 351-357 | DOI | MR

Cited by Sources: