余秩和模态至多为2的复奇异性分类算法
A Classification Algorithm for Complex Singularities of Corank and Modality up to Two
摘要：
In（Arnold，1985），V.I.阿诺德已经获得了正规形式，并开发了一个分类器，特别是，所有孤立的超曲面奇点超过复数模态2。基于一系列的105个定理，这个分类器确定了给定奇点的类型。然而，对于正模态，这并不固定奇异性的右等价类，因为没有指定模参数的值。本文提出了一个简单的分类算法，用于孤立的超曲面奇点的corank和模态多达两个。对于由有理数上的多项式给出的奇异性，该算法通过在Arnold规范形列表中指定多项式代表来确定其右等价类。
英文摘要：
In (Arnold, 1985), V.I. Arnold has obtained normal forms and has developed a classifier for, in particular, all isolated hypersurface singularities over the complex numbers up to modality 2. Building on a series of 105 theorems, this classifier determines the type of the given singularity. However, for positive modality, this does not fix the right equivalence class of the singularity, since the values of the moduli parameters are not specified. In this paper, we present a simple classification algorithm for isolated hypersurface singularities of corank and modality up to two. For a singularity given by a polynomial over the rationals, the algorithm determines its right equivalence class by specifying a polynomial representative in Arnold's list of normal forms.
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