Equisingularity of families of map germs between curves |
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Authors: | J J Nu?o-Ballesteros J N Tomazella |
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Institution: | 1. Departament de Geometria i Topologia, Universitat de València, Campus de Burjassot, 46100, Burjassot, Spain 2. Departamento de Matemática, Universidade Federal de S?o Carlos, Caixa Postal 676, 13560-905, S?o Carlos, SP, Brazil
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Abstract: | Given a finite map germ f : (X, 0) → (Y, 0) between complex analytic reduced space curves, we look at invariants which control the topological triviality and the Whitney equisingularity in families of this type of map germs. In the case that (Y, 0) is smooth, the main invariant is the Milnor number of a function on a curve. We deduce some applications to the equisingularity of families of finitely determined map germs ${f : (\mathbb{C}^2, 0) \to (\mathbb{C}^2, 0)}$ and ${f : (\mathbb{C}^2, 0) \to (\mathbb{C}^3, 0)}$ . |
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