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 $\widetilde{b}$ and the value set of differentials $\Lambda$ for plane branches. For plane branches defined by semiquasihomogeneous polynomial we describe the set of common roots of $\widetilde{b}$ sharing by every branch with a fixed $\Lambda$ set.