Versions of injectivity  and extension theorems

Gongyo, Yoshinori; ichi Matsumura, Shin

doi:10.24033/asens.2325

Versions of injectivity and extension theorems
[Versions des théorèmes d'injectivité et d'extension]

Gongyo, Yoshinori ; ichi Matsumura, Shin

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 2, pp. 479-502.

Résumé
Abstract

Nous donnons une version analytique du théorème d'injectivité en utilisant les idéaux multiplicateurs, et démontrons des théorèmes d'extension pour le faisceau adjoint d'une paire dlt. De plus nous obtenons des résultats de semi-amplitude liés à la conjecture d'abondance en géométrie birationnelle et la conjecture de semi-amplitude pour les variétés hyperkählériennes.

We give an analytic version of the injectivity theorem by using multiplier ideal sheaves of singular hermitian metrics, and prove extension theorems for the log canonical bundle of dlt pairs. Moreover we obtain partial results related to the abundance conjecture in birational geometry and the semi-ampleness conjecture for hyperKähler manifolds.

Publié le : 2017-11-12

MR Zbl

DOI : 10.24033/asens.2325

Classification : 14E30, 14F18, 32L10, 32L20, 32J25.
Keywords: Injectivity theorem, extension theorem, abundance conjecture.
Mot clés : Théorème d'injectivité, théorème d'extension, conjecture d'abondance.

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     author = {Gongyo, Yoshinori and ichi Matsumura, Shin},
     title = {Versions of injectivity  and extension theorems},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {479--502},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 50},
     number = {2},
     year = {2017},
     doi = {10.24033/asens.2325},
     mrnumber = {3621435},
     zbl = {1401.14083},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.2325/}
}

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Gongyo, Yoshinori; ichi Matsumura, Shin. Versions of injectivity  and extension theorems. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 2, pp. 479-502. doi : 10.24033/asens.2325. http://archive.numdam.org/articles/10.24033/asens.2325/

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