open access

https://doi.org/10.14943/49128

https://hdl.handle.net/2115/45526

A factorization theorem for unfoldings of analytic functions

英語

53-xx DIFFERENTIAL GEOMETRY

1987-07

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

8

2-10

Let f and g be holomorphic function germs at 0 in C n x c l = {(x,s)} If dxg ∧ dxf = O and if f(x) = f(x,O) is not a power or a unit, then there exists a germ λ at O in C x C l such that g(x,s) = λ(f(x,s),s) . 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. The notion of an RL-morphism in the unfolding theory of foliation singularities was introduced in [5] to describe the determinacy results and in [6] the versality theorem for these morphisms is proved. This note, which should be considered as an appendix to [5] or [6], contains a factorization theorem implying that an RL-morphism is a generalization of a right-left morphism in the unfolding theory of function germs. It depends on the Mattei-Moussu factorization theorem ([1]) and is a generalization of a result of Moussu [2].

紀要論文

Version of Record