Topological type of discriminants of some special families

被引:0
|
作者
Evelia R. García Barroso
M. Fernando Hernández Iglesias
机构
[1] Universidad de La Laguna,Dpto. Matemáticas, Estadística e I.O. Sección de Matemáticas
[2] Universidad Nacional Mayor de San Marcos,Facultad de Ciencias Matemáticas, Escuela de Matemática
[3] Pontificia Universidad Católica del Perú,Dpto. Ciencias
来源
Periodica Mathematica Hungarica | 2022年 / 84卷
关键词
Discriminant curve; Nondegenerate singularity; Newton polygon; Zariski invariant; Milnor number; Tjurina number; Primary 14J17; Secondary 32S15;
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学科分类号
摘要
We will describe the topological type of the discriminant curve of the morphism (ℓ,f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\ell , f)$$\end{document}, where ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document} is a smooth curve and f is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch.
引用
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页码:321 / 345
页数:24
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