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March 2022 Local theory of singularities of three functions and the product maps
Kazuto Takao
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Hiroshima Math. J. 52(1): 53-91 (March 2022). DOI: 10.32917/h2021020

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

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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

Information

Received: 22 March 2021; Revised: 7 November 2021; Published: March 2022
First available in Project Euclid: 25 March 2022

Digital Object Identifier: 10.32917/h2021020

Subjects:
Primary: 57R45

Keywords: singular surface , singularity of smooth map

Rights: Copyright © 2022 Hiroshima University, Mathematics Program

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Vol.52 • No. 1 • March 2022
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