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A factorization theorem for unfoldings of analytic functions

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/49128

Title: A factorization theorem for unfoldings of analytic functions
Authors: Suwa, Tatsuo Browse this author
Keywords: 53-xx DIFFERENTIAL GEOMETRY
Issue Date: Jul-1987
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 8
Start Page: 2
End Page: 10
Abstract: 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].
Type: bulletin (article)
URI: http://eprints3.math.sci.hokudai.ac.jp/904/
http://hdl.handle.net/2115/45526
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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