On the quasi-ordinary cuspidal foliations in ( C3, 0 )

In this paper, we study a class of singularities of codimension 1 holomorphic germs of foliations in ( C3, 0 ), namely those ones having only one separatrix, that is a quasi-ordinary surface, and whose reduction of singularities agrees with the combinatorial desingularization of the separatrix. We show that the analytic classification of these germs can be read in the holonomy of a certain component of the exceptional divisor of the desingularization. © 2005 Elsevier Inc. All rights reserved.