no. 4
On the moduli b-divisors of lc-trivial fibrations
[Sur les b-diviseurs de modules des fibrations lc-triviales]
Fujino, Osamu1 ; Gongyo, Yoshinori2, 3
1 Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
2 Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK
3 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914 Japan.
Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1721-1735.

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.

DOI : 10.5802/aif.2894
Classification : 14N30, 14E30, 14J10
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

Fujino, Osamu 1 ; Gongyo, Yoshinori 2, 3

1 Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
2 Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK
3 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914 Japan. 
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Fujino, Osamu; Gongyo, Yoshinori. On the moduli b-divisors of lc-trivial fibrations. Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1721-1735. doi : 10.5802/aif.2894. https://aif.centre-mersenne.org/articles/10.5802/aif.2894/

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