Analytic Normal Forms of Germs of Holomorphic Dicritic Foliations

We consider the class $\mathbf V_{n+1}^d$ of dicritic germs of holomorphic vector fields in $(\mathbf C^2,0)$ with vanishing $n$-jet at the origin, $n\ge1$, and their generated foliations. Earlier we proved that under some genericity assumptions, the formal equivalence of two germs implies their analytic equivalence and formal normal forms of germs in $\mathbf V_{n+1}^d$ were given. In this work we give analytic normal forms of generic germs of dicritic foliations of $\mathbf V_{n+1}^d$.