Abstract
We will show that for each k≠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.
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Acknowledgments
The second author is partially supported by the Grant-in-Aid for Scientific Research (C), JSPS KAKENHI Grant Number 25400078 and the Kawai Fund for Mathematical Sciences.
The fourth author is partially supported by the Vietnam institute for Advance study in Mathematics (VIASM).
The second and fourth authors are partially supported by the JSPS Postdoctoral Fellowship for Foreign Researchers’ Grant-in-Aid 25/03014.
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Inaba, K., Ishikawa, M., Kawashima, M. et al. On Innermost Circles of the Sets of Singular Values for Generic Deformations of Isolated Singularities. Acta Math Vietnam 42, 237–247 (2017). https://doi.org/10.1007/s40306-016-0200-1
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DOI: https://doi.org/10.1007/s40306-016-0200-1