Action of the Cremona group on foliations on ${\mathbb{P}}_{\mathbb{C}}^2$: some curious facts

Dominique Cerveau, Julie Déserti

The Cremona group of birational transformations of ${\mathbb{P}}_{\mathbb{C}}^2$ acts on the space $\mathbb{F}(2)$ of holomorphic foliations on the complex projective plane. Since this…