Bernstein polynomial and value set of differentials for plane branches

Abstract

In this work, we study the relation between the roots of the Bernstein polynomial $\tilde{b}$ and the value set of differentials $\hat{I}›$ for plane branches. For plane branches defined by semiquasihomogeneous polynomial we describe the set of common roots of $\tilde{b}$ sharing by every branch with a fixed $\hat{I}›$ set.