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A factorization theorem for unfoldings of analytic functions
| Title: | A factorization theorem for unfoldings of analytic functions |
| Authors: | Suwa, Tatsuo Browse this author |
| Keywords: | 53-xx DIFFERENTIAL GEOMETRY |
| Issue Date: | Jul-1987 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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