Kodai Mathematical Journal

On the number of cusps of perturbations of complex polynomials

Kazumasa Inaba

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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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Kodai Math. J., Volume 42, Number 3 (2019), 593-610.

First available in Project Euclid: 31 October 2019

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Inaba, Kazumasa. On the number of cusps of perturbations of complex polynomials. Kodai Math. J. 42 (2019), no. 3, 593--610. doi:10.2996/kmj/1572487234. https://projecteuclid.org/euclid.kmj/1572487234

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