Abundance for Kähler threefolds

Campana, Frédéric; Höring, Andreas; Peternell, Thomas

doi:10.24033/asens.2301

Abundance for Kähler threefolds
[Abondance pour les variétés kälhériennes de dimension 3]

Campana, Frédéric ; Höring, Andreas ; Peternell, Thomas

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 4, pp. 971-1025.

Résumé
Abstract

Soit $X$ une variété kählérienne compacte à singularités terminales. Si $K_{X}$ est nef, nous montrons que $K_{X}$ est semi-ample, c'est-à-dire qu'un multiple $m K_{X}$ est engendré par ses sections globales.

Let $X$ be a compact Kähler threefold with terminal singularities such that $K_{X}$ is nef. We prove that $K_{X}$ is semiample, i.e., some multiple $m K_{X}$ is generated by global sections.

Publié le : 2016-11-12

MR Zbl

DOI : 10.24033/asens.2301

Classification : 32J27, 14E30, 14J30, 32J17, 32J25.
Keywords: log MMP, cone theorem, contraction theorem, rational curves, Zariski decomposition, Kähler manifolds, abundance.
Mot clés : log MMP, théorème du cône, théorème de contraction, courbes rationnelles, décomposition de Zariski, variétés kählériennes, abondance.

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     author = {Campana, Fr\'ed\'eric and H\"oring, Andreas and Peternell, Thomas},
     title = {Abundance for {K\"ahler} threefolds},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {971--1025},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 49},
     number = {4},
     year = {2016},
     doi = {10.24033/asens.2301},
     mrnumber = {3552019},
     zbl = {1386.32020},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.2301/}
}

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Campana, Frédéric; Höring, Andreas; Peternell, Thomas. Abundance for Kähler threefolds. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 4, pp. 971-1025. doi : 10.24033/asens.2301. http://www.numdam.org/articles/10.24033/asens.2301/

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