Modules formels locaux de feuilletages holomorphes

We give a complete list of formal invariants for a large class of formal differential 1-forms $\text{w}\in \mathbb{C}[[x,y]]dx+\mathbb{C}[[x,y]]dy$. \indent A $\widehat{SL}$-equisingular deformation is an equireducible deformation which leaves invariant both the local formal types and the holonomy representation of the components of the exceptional divisor. We characterize the 1-forms with finite formal type (t.f.f), i.e. those which admit a semi-universal $\widehat{SL}$-equisingular deformation, and we give an explicit combinatorial criterion of finiteness. \indent The set of 1-forms with finite formal type contains a dense open set (in the sense of Krull’s topology)in the set of 1-forms of the second kind.