On the zeros and critical points of a rational map (Q1598307)

Let \(f:{\mathbf P}^1\to{\mathbf P}^1\) be a rational map, \(\{\alpha_i\}_{i\in I}\) the set of zeros of \(f\), \(\{w_j\}_{j\in J}\) the set of critical points of \(f\) which are not zeros of \(f\). The paper studies the relations between the points \(\alpha_i\) and the points \(w_j\), weighted with their multiplicities. Some geometrical interpretations of these relations are also given.