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Commentarii Mathematici Helvetici

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Volume 88, Issue 2, 2013, pp. 305–321
DOI: 10.4171/CMH/286

Published online: 2013-04-24

Degenerate singularities of one dimensional foliations

Viviana Ferrer[1] and Israel Vainsencher[2]

(1) Universidade Federal Fluminense, NiterĂ³i, 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