Simple Singularities of Mappings C, 0 → C2, 0
Simple Singularities of Mappings C, 0 → C2, 0
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映射的简单奇点 C, 0 → C2, 0
DOI：
10.1112/jlms/s2-26.3.465
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发表时间：
1982
影响因子：
1.2
通讯作者：
T. Gaffney
中科院分区：
文献类型：
--
作者：
John W. Bruce;T. Gaffney
就简单性质而言，VI Arnol'd 发现的函数的简单奇点一直是人们非常感兴趣的对象。对于Mather 讨论的任何群Sf, &, si, JT（比如$），我们可以定义$ 简单映射胚芽k", 0-> kp, 0 的概念，其中k 是U 或C。在本文中，我们将si 简单胚芽C, 0-·C2, 0 分类。（真实情况类似，但我们省略细节。）我们解决这个问题的最初方法是在射流空间Jfc (l, 2) 中工作。事实上，这就是如何然而，我们首先获得了我们的列表，在代数曲线的参数化 (j): C, 0-> C2, 0 和这些曲线的定义方程之间存在密切的联系。这种联系值得研究，并且使用 [1] 中的 Arnol'd 函数分类，我们将在第 3 节中通过考虑定义来导出 si 简单细菌 C, 0-> C2, 0 的列表。在第 2 节中，我们将考虑参数化、其定义方程和变形之间的联系，L. Rudolph [7] 通过不同方式获得了第一作者对 IHES 访问的财政支持，我们也感谢 CTC Wall 提供的一些有用的评论。
The simple singularities of functions discovered, in so far as the property of being simple is concerned, by VI Arnol'd have been the object of much interest. For any of the groups Sf, &, si, JT (say $) discussed by Mather one can define the notion of a $ simple map germ k", 0-> kp, 0 where k is U or C. In this paper we classify si simple germs C, 0-• C2, 0.(The real case is similar but we omit the details.) Our original approach to this problem was to work in the jet space Jfc (l, 2). Indeed this was how we first obtained our list. There is, however, a close connection between germs^ giving parametrizations (j): C, 0-> C2, 0 of germs of algebraic curves and the defining equations of these curves,/= 0. This connection is worthy of study and using Arnol'd's classification of functions in [1] we shall, in § 3, derive our list of si simple germs C, 0-> C2, 0 by considering the defining equations of their images. In § 2 we shall consider the connection between the parametrizations, their defining equations and deformations of such. Results related to ours have been obtained by different means by L. Rudolph [7]. The first author gratefully acknowledges the financial support of the Stiftung Volkswagenwerk for a visit to the IHES, and both authors acknowledge the financial support of the Science Research Council. We are also grateful to CTC Wall for some helpful comments.