Commentarii Mathematici Helvetici
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Published online: 2013-04-24
Degenerate singularities of one dimensional foliationsViviana Ferrer and Israel Vainsencher (1) Universidade Federal Fluminense, Niterói, Brazil
(2) Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
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.
Keywords: Holomorphic foliation, singularities, enumerative geometry
Ferrer Viviana, Vainsencher Israel: Degenerate singularities of one dimensional foliations. Comment. Math. Helv. 88 (2013), 305-321. doi: 10.4171/CMH/286