Journal of Prime Research in Mathematics
Vol. 1 (2008), Issue 1, pp. 0148 – 153
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
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
Copyright © 2008 Zahid Raza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2008.
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.