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A factorization theorem for unfoldings of analytic functions

Author: Tatsuo Suwa
Journal: Proc. Amer. Math. Soc. 104 (1988), 131-134
MSC: Primary 58H15; Secondary 32G07
MathSciNet review: 958056
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Abstract: Let $ \tilde f$ and $ g$ be holomorphic function germs at 0 in $ {{\mathbf{C}}^n} \times {{\mathbf{C}}^n} = \left\{ {\left( {x,s} \right)} \right\}$. If $ {d_x}g\Lambda {d_x}\tilde f = 0$ and if $ f\left( x \right) = \tilde f\left( {x,0} \right)$ is not a power or a unit, then there exists a germ $ \lambda $ at 0 in $ {{\mathbf{C}}^n} \times {{\mathbf{C}}^n}$ such that $ g\left( {x,s} \right) = \lambda \left( {\tilde f\left( {x,s} \right),s} \right)$. The result has the implication that the notion of an RL-morphism in the unfolding theory of foliation germs generalizes that of a right-left morphism in the function germ case.

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Article copyright: © Copyright 1988 American Mathematical Society