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.
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