Abstract
Suppose that a smooth map $(f,g,h):\mathbb{R}^n \rightarrow \mathbb{R}^3$, where $n \geq3$, has a stable singularity at the origin. We characterize the stability of the function $f:\mathbb{R}^n \rightarrow \mathbb{R}$ and the map $(f,g):\mathbb{R}^n \rightarrow \mathbb{R}^2$ at the origin in terms of the discriminant set of $(f,g,h)$.
Funding Statement
The author was supported by JSPS KAKENHI Grant Number 26800042.
Acknowledgement
The author would like to thank Kentaro Saji for valuable discussions and conversations. He was also supported by JSPS and CAPES under the Japan– Brazil research cooperative program, and supported by the Research Institute for Mathematical Sciences, a Joint Usage/Research Center located in Kyoto University.
Citation
Kazuto Takao. "Local theory of singularities of three functions and the product maps." Hiroshima Math. J. 52 (1) 53 - 91, March 2022. https://doi.org/10.32917/h2021020
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