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On Innermost Circles of the Sets of Singular Values for Generic Deformations of Isolated Singularities

Kazumasa Inaba , $icon-email$ Masaharu Ishikawa , Masayuki Kawashima , Nguyen Tat Thang

Abstract

We will show that for each $k \neq 1$ , there exists an isolated singularity of a real analytic map from $R^{4}$ to $R^{2}$ which admits a real analytic deformation such that the set of singular values of the deformed map has a simple, innermost component with $k$ outward cusps and no inward cusps. Conversely, such a singularity does not exist if $k = 1$ .

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On Innermost Circles of the Sets of Singular Values for Generic Deformations of Isolated Singularities

Abstract