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

In: Singularities and Computer Algebra

Author

Listed:
  • Janko Böhm

    (University of Kaiserslautern, Department of Mathematics)

  • Magdaleen S. Marais

    (University of Pretoria, Department of Mathematics and Applied Mathematics)

  • Gerhard Pfister

    (University of Kaiserslautern, Department of Mathematics)

Abstract

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.

Suggested Citation

  • Janko Böhm & Magdaleen S. Marais & Gerhard Pfister, 2017. "A Classification Algorithm for Complex Singularities of Corank and Modality up to Two," Springer Books, in: Wolfram Decker & Gerhard Pfister & Mathias Schulze (ed.), Singularities and Computer Algebra, pages 21-46, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-28829-1_2
    DOI: 10.1007/978-3-319-28829-1_2
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