## Kodai Mathematical Journal

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

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.kmj/1572487234

**Digital Object Identifier**

doi:10.2996/kmj/1572487234

**Mathematical Reviews number (MathSciNet)**

MR4025760

#### Citation

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