English

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

Algebraic Geometry 2019-08-15 v2 Commutative Algebra

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.

Keywords

Cite

@article{arxiv.1604.04774,
  title  = {A Classification Algorithm for Complex Singularities of Corank and Modality up to Two},
  author = {Janko Boehm and Magdaleen S. Marais and Gerhard Pfister},
  journal= {arXiv preprint arXiv:1604.04774},
  year   = {2019}
}

Comments

19 pages, 5 figures, minor revisions

R2 v1 2026-06-22T13:33:56.032Z