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Unfoldings of foliations with multiform first integrals

Tatsuo Suwa — 1983

Annales de l'institut Fourier

Let F = ( ω ) be a codim 1 local foliation generated by a germ ω of the form ω = f 1 ... f p i = 1 p λ i d f i f i for some complex numbers λ i and germs f i of holomorphic functions at the origin in C n . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of F . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for F is equivalent to the unfolding theory for the multiform function...

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