  Here we state a conjecture concerning a local version of Brunella's
alternative: any codimension one foliation in $({\mathbb C}^3,0)$ without germ
of invariant surface has a neighborhood of the origin formed by leaves
containing a germ of analytic curve at the origin. We prove the conjecture for
the class of codimension one foliations whose reduction of singularities is
obtained by blowing-up points and curves of equireduction and such that the
final singularities are free of saddle-nodes. The concept of "partial
separatrix" for a given reduction of singularities has a central role in our
argumentations, as well as the quantitative control of the generic Camacho-Sad
index in dimension three. The "nodal components" are the only possible
obstructions to get such germs of analytic curves. We use the partial
separatrices to push the leaves near a nodal component towards compact
diacritical divisors, finding in this way the desired analytic curves.
