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.
Revised:
Accepted:
Published online:
Keywords: log canonical ring, plt, canonical bundle formula
Mot clés : anneau log canonique, plt, formule du fibré canonique
Fujino, Osamu 1; Liu, Haidong 2
@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] Weak semistable reduction in characteristic 0, Invent. Math., Volume 139 (2000) no. 2, pp. 241-273 | DOI | MR
[2] Shokurov’s boundary property, J. Differ. Geom., Volume 67 (2004) no. 2, pp. 229-255 | MR
[3] 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] 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] Fundamental theorems for the log minimal model program, Publ. Res. Inst. Math. Sci., Volume 47 (2011) no. 3, pp. 727-789 | DOI | MR
[6] Minimal model theory for log surfaces, Publ. Res. Inst. Math. Sci., Volume 48 (2012) no. 2, pp. 339-371 | DOI | MR
[7] 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] Foundations of the minimal model program, MSJ Memoirs, 35, Mathematical Society of Japan, 2017, xv+289 pages | MR | Zbl
[9] Fundamental properties of basic slc-trivial fibrations I (2018) (https://arxiv.org/abs/1804.11134, to appear in Publ. Res. Inst. Math. Sci.)
[10] Fundamental properties of basic slc-trivial fibrations II (2018) (https://arxiv.org/abs/1808.10604, to appear in Publ. Res. Inst. Math. Sci.)
[11] On the moduli b-divisors of lc-trivial fibrations, Ann. Inst. Fourier, Volume 64 (2014) no. 4, pp. 1721-1735 | DOI | Numdam | MR
[12] 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] A canonical bundle formula, J. Differ. Geom., Volume 56 (2000) no. 1, pp. 167-188 | MR | Zbl
[14] Minimal model theory for relatively trivial log canonical pairs, Ann. Inst. Fourier, Volume 68 (2018) no. 5, pp. 2069-2107 | DOI | Numdam | MR
[15] Log canonical models of algebraic -folds, Int. J. Math., Volume 3 (1992) no. 3, pp. 351-357 | DOI | MR
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