Manifolds of low dimension with trivial canonical bundle in Grassmannians

Vladimiro Benedetti (1)

1 I2M - Institut de Mathématiques de Marseille

We study fourfolds with trivial canonical bundle which are zero loci of sections of homogeneous, completely reducible bundles over ordinary and classical complex Grassmannians. We prove that the only HyperKähler fourfolds among them are the example of Beauville and Donagi, and the example of Debarre and Voisin. In doing so, we give a complete classification of those varieties. We include also the analogous classification for surfaces and threefolds.

Domaines: Géométrie algébrique [math.AG]

Vladimiro Benedetti. Manifolds of low dimension with trivial canonical bundle in Grassmannians. Mathematische Zeitschrift, 2018. ⟨hal-01362172v3⟩