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 $\mathbf{R}^2$.
Citation
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