An example of a non-algebraizable singularity of a holomorphic foliation

Valente Ramirez (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We say that the the germ of a singular holomorphic foliation on $(\mathbb{C}^2,0)$ is algebraizable whenever it is holomorphically conjugate to the singularity of a foliation defined globally on a projective algebraic surface. The object of this work is to construct a concrete example of a non--algebraizable singularity. Previously only existential results were known.

Domaines: Variables complexes [math.CV]

Valente Ramirez. An example of a non-algebraizable singularity of a holomorphic foliation. L'Enseignement Mathématique , 2016, 62 (1-2), pp.7-14. ⟨10.4171/LEM/62-1/2-3⟩. ⟨hal-02373652⟩