Albanese maps of projective manifolds with nef anticanonical bundles

Cao, Junyan

doi:10.24033/asens.2405

Albanese maps of projective manifolds with nef anticanonical bundles
[Application d'Albanese de variétés projectives à fibrés anticanoniques nef]

Cao, Junyan

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 5, pp. 1137-1154.

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Résumé
Abstract

Soit $X$ une variété projective à fibré anticanonique nef. On montre que l'application d'Albanese $p : X \to Y$ est localement triviale. En particulier, $p$ est lisse.

Let $X$ be a projective manifold such that the anticanonical bundle $- K_{X}$ is nef. We prove that the Albanese map $p : X \to Y$ is locally trivial. In particular, $p$ is a submersion.

Publié le : 2019-11-12

MR Zbl

DOI : 10.24033/asens.2405

Classification : 32J27; 32Qxx.
Keywords: Nef anticanonical bundle, Albanese map, positivity of direct images.
Mot clés : Fibré anticanonique nef, application d'Albanese, positivité de l'image directe

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     title = {Albanese maps of projective manifolds with nef anticanonical bundles},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1137--1154},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 52},
     number = {5},
     year = {2019},
     doi = {10.24033/asens.2405},
     mrnumber = {4057779},
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Cao, Junyan. Albanese maps of projective manifolds with nef anticanonical bundles. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 5, pp. 1137-1154. doi : 10.24033/asens.2405. http://archive.numdam.org/articles/10.24033/asens.2405/

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