no. 4
Algebraic geometry
Nefness: Generalization to the lc case
[Nefness : Généralisation au cas lc]

Présenté par : Claire Voisin

Comptes Rendus. Mathématique, Tome 352 (2014) no. 4, pp. 333-337.

Cette note se consacre à démontrer que la partie modulaire de la formule du fibré canonique pour une fibration qui est lc-triviale et non klt-triviale est b-semiample. Ce résultat est démontré dans [3, §8] et dans [4] en utilisant des resultats très profonds concernant les variations de structure de Hodge mixte. On présente ici une preuve qui est plus élémentaire et qui suit celle de [2, théorème 0.2].

This note is devoted to a proof of the b-nefness of the moduli part in the canonical bundle formula for an lc-trivial fibration that is lc and not klt over the generic point of the base. This result is proved in [3, §8] and [4] by using the theory of variation of mixed Hodge structure. Here we present a proof that makes use only of the theory of variation of Hodge structure and follows Ambro's proof of [2, Theorem 0.2].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.01.011 
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Floris, Enrica. Nefness: Generalization to the lc case. Comptes Rendus. Mathématique, Tome 352 (2014) no. 4, pp. 333-337. doi : 10.1016/j.crma.2014.01.011. http://www.numdam.org/articles/10.1016/j.crma.2014.01.011/

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