Degenerate singularities of one dimensional foliations

Abstract

We give formulas for the degrees of the spaces of holomorphic foliations in the complex projective plane with a dicritical singularity of prescribed order. Blowing up such singularity induces, generically, a foliation with only finitely many leaves tangent to the exceptional line; we find the degree of the locus defined by imposing a leaf of total contact with the exceptional line.