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October 2019 On the number of cusps of perturbations of complex polynomials
Kazumasa Inaba
Kodai Math. J. 42(3): 593-610 (October 2019). DOI: 10.2996/kmj/1572487234

Abstract

Let $f$ be a 1-variable complex polynomial such that $f$ has an isolated singularity at the origin. In the present paper, we show that there exists a perturbation $f_{t}$ of $f$ which has only fold singularities and cusps as singularities of a real polynomial map from $\mathbf{R}^2$ to $\mathbf{R}^2$. We then calculate the number of cusps of $f_t$ in a sufficiently small neighborhood of the origin and estimate the number of cusps of $f_t$ in $\mathbf{R}^2$.

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Kazumasa Inaba. "On the number of cusps of perturbations of complex polynomials." Kodai Math. J. 42 (3) 593 - 610, October 2019. https://doi.org/10.2996/kmj/1572487234

Information

Published: October 2019
First available in Project Euclid: 31 October 2019

zbMATH: 07174417
MathSciNet: MR4025760
Digital Object Identifier: 10.2996/kmj/1572487234

Rights: Copyright © 2019 Tokyo Institute of Technology, Department of Mathematics

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Vol.42 • No. 3 • October 2019
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