Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro’s result on klt-trivial fibrations.
Grosso modo, en utilisant le programme des modèles minimaux semi-stables, nous montrons que la partie modulaire d’une fibration lc-triviale coïncide avec celle d’une fibration klt-triviale induite par adjonction aprés changement de base par un morphisme génériquement fini. Comme application, eu utilisant le résultat de Ambro sur fibrations klt-triviales, on obtient que la partie modulaire d’une fibration lc-triviale est b-nef et abondante.
Keywords: semi-stable minimal model program, canonical bundle formulae, lc-trivial fibrations, klt-trivial fibrations
Mot clés : programme des modèles minimaux semi-stables, formules de fibré canoniques, fibrations lc-triviales, fibrations klt-triviales
@article{AIF_2014__64_4_1721_0, author = {Fujino, Osamu and Gongyo, Yoshinori}, title = {On the moduli b-divisors of lc-trivial fibrations}, journal = {Annales de l'Institut Fourier}, pages = {1721--1735}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {4}, year = {2014}, doi = {10.5802/aif.2894}, zbl = {06387321}, mrnumber = {3329677}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2894/} }
TY - JOUR AU - Fujino, Osamu AU - Gongyo, Yoshinori TI - On the moduli b-divisors of lc-trivial fibrations JO - Annales de l'Institut Fourier PY - 2014 SP - 1721 EP - 1735 VL - 64 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2894/ DO - 10.5802/aif.2894 LA - en ID - AIF_2014__64_4_1721_0 ER -
%0 Journal Article %A Fujino, Osamu %A Gongyo, Yoshinori %T On the moduli b-divisors of lc-trivial fibrations %J Annales de l'Institut Fourier %D 2014 %P 1721-1735 %V 64 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2894/ %R 10.5802/aif.2894 %G en %F AIF_2014__64_4_1721_0
Fujino, Osamu; Gongyo, Yoshinori. On the moduli b-divisors of lc-trivial fibrations. Annales de l'Institut Fourier, Volume 64 (2014) no. 4, pp. 1721-1735. doi : 10.5802/aif.2894. http://www.numdam.org/articles/10.5802/aif.2894/
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