[Un théorème de décomposition pour les variétés à singularités lissables dont la première classe de Chern est nulle]
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.
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.
Accepté le :
Publié le :
DOI : 10.5802/jep.65
Keywords: Varieties with trivial canonical divisor, smoothable klt singularities, Kähler-Einstein metrics on smoothable spaces
Mot clés : Variétés dont le diviseur canonique est trivial, singularités klt lissables, métriques de Kähler-Einstein sur les espaces lissables
Stéphane Druel 1 ; Henri Guenancia 2
CC-BY-ND 4.0
@article{JEP_2018__5__117_0,
author = {St\'ephane Druel and Henri Guenancia},
title = {A decomposition theorem for smoothable~varieties with trivial~canonical~class},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {117--147},
publisher = {\'Ecole polytechnique},
volume = {5},
year = {2018},
doi = {10.5802/jep.65},
zbl = {06988575},
mrnumber = {3732694},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.65/}
}
TY - JOUR AU - Stéphane Druel AU - Henri Guenancia TI - A decomposition theorem for smoothable varieties with trivial canonical class JO - Journal de l’École polytechnique — Mathématiques PY - 2018 SP - 117 EP - 147 VL - 5 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.65/ DO - 10.5802/jep.65 LA - en ID - JEP_2018__5__117_0 ER -
%0 Journal Article %A Stéphane Druel %A Henri Guenancia %T A decomposition theorem for smoothable varieties with trivial canonical class %J Journal de l’École polytechnique — Mathématiques %D 2018 %P 117-147 %V 5 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.65/ %R 10.5802/jep.65 %G en %F JEP_2018__5__117_0
Stéphane Druel; Henri Guenancia. 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. https://jep.centre-mersenne.org/articles/10.5802/jep.65/
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