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:


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 \(t\).


Pane curves, polar curves, discriminant.