Determinacy of complex analytic foliation germs without integrating factors

Cerveau, Dominique; Suwa, Tatsuo

doi:10.1090/S0002-9939-1991-1072331-0

Determinacy of complex analytic foliation germs without integrating factors
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by Dominique Cerveau and Tatsuo Suwa PDF

Proc. Amer. Math. Soc. 112 (1991), 989-997 Request permission

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.

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