Generalized Poincaré-Dulac singularities of holomorphic foliations

Abstract

In this paper, we study the analytic classification of a class of nilpotent singularities of holomorphic foliations in $({\mathbb{C}}^2,0)$, those exhibiting a Poincaré-Dulac type singularity in their reduction process. This analytic classification is based in the holonomy of a certain component of the exceptional divisor. Finally, as a consequence, we show that these singularities exhibit a formal analytic rigidity.

15 pages