Article Dans Une Revue Inventiones Mathematicae Année : 2018

A decomposition theorem for singular spaces with trivial canonical class of dimension at most five

Stéphane Druel

Résumé

In this paper we partly extend the Beauville-Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical 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 holomorphic symplectic varieties.

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hal-01990824 , version 1 (09-10-2022)

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Stéphane Druel. A decomposition theorem for singular spaces with trivial canonical class of dimension at most five. Inventiones Mathematicae, 2018, 211 (1), pp.245-296. ⟨10.1007/s00222-017-0748-y⟩. ⟨hal-01990824⟩
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