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

Stéphane Druel (1)

1 IF - Institut Fourier

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.

Domaines: Géométrie algébrique [math.AG]

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⟩