A Classification Algorithm for Complex Singularities of Corank and Modality up to Two

Abstract

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.

arXiv comment19 pages, 5 figures, minor revisions

References in corpus (3)

• The Classification of Real Singularities Using SINGULAR. Part I: Splitting Lemma and Simple Singularities
• The Classification of Real Singularities Using SINGULAR. Part II: The Structure of the Equivalence Classes of the Unimodal Singularities
• The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2

Cited by in corpus (1)

• The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2