Factorization of the polar curve and the Newton polygon (Q1876295)

Consider \(f\in \mathbb C\{X,Y\}\), which has an isolated singularity. Consider a line \(bX-aY=0\) which is not tangent to \(f=0\), and consider the generic polar \( \partial f:=a \frac{\partial f}{\partial x} + b \frac{\partial f}{\partial y}\). In this paper the authors study the factorization of \(\partial f\) using the Newton polygon of \(f\). As an application they calculate the minimal polar invariant and prove a bound on the number of special values in the pencil \(f -t\ell^N\).