A decomposition theorem for smoothable varieties with trivial canonical class

Druel, Stéphane; Guenancia, Henri

doi:10.5802/jep.65

Geodesic

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A decomposition theorem for smoothable varieties with trivial canonical class
[Un théorème de décomposition pour les variétés à singularités lissables dont la première classe de Chern est nulle]

Druel, Stéphane ¹ ; Guenancia, Henri ²

¹ Institut Fourier, UMR 5582 du CNRS, Université Grenoble Alpes CS 40700, 38058 Grenoble cedex 9, France
² Department of Mathematics, Stony Brook University Stony Brook, NY 11794-3651, United States

Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 117-147.

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Abstract (VO)
Résumé

In this paper we show that any smoothable complex projective variety, smooth in codimension two, with klt singularities and numerically trivial canonical class admits a finite cover, étale in codimension one, that decomposes as a product of an abelian variety, and singular analogues of irreducible Calabi-Yau and irreducible symplectic varieties.

Nous montrons que toute variété complexe projective, à singularités klt lissables et lisse en codimension deux, dont le diviseur canonique est numériquement trivial, admet un revêtement quasi-étale fini qui se décompose en un produit d’une variété abélienne et d’analogues singuliers des variétés symplectiques irréductibles et des variétés de Calabi-Yau irréductibles.

Reçu le : 2017-05-10
Accepté le : 2017-11-17
Publié le : 2017-11-29

MR Zbl

DOI : 10.5802/jep.65

Classification : 14J32, 14E30
Keywords: Varieties with trivial canonical divisor, smoothable klt singularities, Kähler-Einstein metrics on smoothable spaces
Mots-clés : Variétés dont le diviseur canonique est trivial, singularités klt lissables, métriques de Kähler-Einstein sur les espaces lissables

Affiliations des auteurs :

Druel, Stéphane ¹ ; Guenancia, Henri ²

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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Druel, Stéphane; Guenancia, Henri. A decomposition theorem for smoothable varieties with trivial canonical class. Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 117-147. doi : 10.5802/jep.65. http://geodesic.mathdoc.fr/articles/10.5802/jep.65/

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