## Kodai Mathematical Journal

### On the number of cusps of perturbations of complex polynomials

Kazumasa Inaba

#### 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 $\mathbf{R}^2$.

#### Article information

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

Dates
First available in Project Euclid: 31 October 2019