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.
Cite this article
Viviana Ferrer, Israel Vainsencher, Degenerate singularities of one dimensional foliations. Comment. Math. Helv. 88 (2013), no. 2, pp. 305–321DOI 10.4171/CMH/286