Fujino, Osamu; Gongyo, Yoshinori
On the moduli b-divisors of lc-trivial fibrations  [ Sur les b-diviseurs de modules des fibrations lc-triviales ]
Annales de l'institut Fourier, Tome 64 (2014) no. 4 , p. 1721-1735
MR 3329677 | Zbl 06387321
doi : 10.5802/aif.2894
URL stable : http://www.numdam.org/item?id=AIF_2014__64_4_1721_0

Classification:  14N30,  14E30,  14J10
Mots clés: programme des modèles minimaux semi-stables, formules de fibré canoniques, fibrations lc-triviales, fibrations klt-triviales
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.
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.

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