Foliations with trivial canonical bundle on Fano 3-folds

Frank Loray (1) , Jorge Vitorio Pereira (2) , Frédéric Touzet (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IMPA - Instituto de Matematica Pura e Aplicada

We classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.

Mots clés: Holomorphic foliation; holomorphic Poisson structure

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]; Géométrie symplectique [math.SG]

Frank Loray, Jorge Vitorio Pereira, Frédéric Touzet. Foliations with trivial canonical bundle on Fano 3-folds. Mathematical News / Mathematische Nachrichten, 2013, 286 (8-9), pp.921-940. ⟨10.1002/mana.201100354⟩. ⟨hal-00694155⟩