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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Determinacy of complex analytic foliation germs without integrating factors


Authors: Dominique Cerveau and Tatsuo Suwa
Journal: Proc. Amer. Math. Soc. 112 (1991), 989-997
MSC: Primary 32L30; Secondary 58C27
MathSciNet review: 1072331
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1072331-0
PII: S 0002-9939(1991)1072331-0
Article copyright: © Copyright 1991 American Mathematical Society