Journal of Prime Research in Mathematics

# Contractible fibers of polynomial functions

Zahid Raza
Abdus Salam School of Mathematical Sciences GC University, 68-B New Muslim Town, Lahore, Pakistan.

$$^{1}$$Corresponding Author: zraza@sms.edu.pk

### Abstract

In this short note, we investigate the topology of complex polynomials $$f(x, y)$$ in two variables. The description of the topology of the corresponding level curves $$C_t : f(x, y) = t$$ is directly related to the vanishing of the leading coefficients cj (t) of the discriminant of the polynomial $$f(x, y) − t$$, regarded as polynomials in $$t$$.

#### Keywords:

Pane curves, polar curves, discriminant.