A Classification Algorithm for Complex Singularities of Corank and Modality up to Two
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In Arnold et al. (Singularities of Differential Maps, vol. I. Birkhäuser, Boston, 1985), 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 ≤ 2 and modality ≤ 2. 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.
KeywordsAlgorithmic classification Arnold normal forms Hypersurface singularities Moduli parameters
2010 Mathematics Subject Classification.Primary 14B05; Secondary 32S25 14Q05
This research was supported by the Staff Exchange Bursary Programme of the University of Pretoria and DFG SPP 1489.
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