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On Innermost Circles of the Sets of Singular Values for Generic Deformations of Isolated Singularities
Kazumasa Inaba
,
Masaharu Ishikawa
,
Masayuki Kawashima
,
Nguyen Tat Thang
Abstract
We will show that for each $k\not =1$, there exists an isolated singularity of a real analytic map from $\mathbb R^4$ to $\mathbb R^2$ 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 $k=1$.