Let F be a holomorphic foliation at p ∈ C2, and let B be a separatrix of F. We prove the
following upper bound GSVp(F, B) ≤ 4τp(F, B)−3μp(F, B), where GSVp(F, B) is the
Gómez-Mont-Seade-Verjovsky index of the foliation F with respect to B, μp(F, B) is the
multiplicity of F along B and τp(F, B) is the dimension of the quotient of C{x, y} by the
ideal generated by the components of any 1-form defining F and any equation of B.
