Determinacy of complex analytic foliation germs without integrating factors

Abstract

It is shown that for a codimension 1 foliation germ without formal integrating factors, the finiteness of the dimension of the space of isomorphism classes of first order unfoldings implies its local finite determinacy. An effective estimate of the order of determinacy is given for general foliation germs in dimension 2. A simple proof for the stability of a foliation germ defined by a simple form in dimension 3 is also included.