The effect of rational maps on polynomial maps
Volume 76 / 2001
Annales Polonici Mathematici 76 (2001), 21-31
MSC: 14D, 14E, 14H.
DOI: 10.4064/ap76-1-3
Abstract
We describe the polynomials $P\in {\mathbb C}[x,y]$ such that $P(1/v^n, A_1v^n + A_2v^{2n} + \dots + A_{m-1}v^{n(m-1)} + v^{nm-k}w) \in {\mathbb C} [v,w]$. As applications we give new examples of bad field generators and examples of families of polynomials with smooth and irreducible fibers.
