On the approximate Jacobian Newton diagrams of an irreducible plane curve

Abstract

We introduce the notion of an approximate Jacobian Newton diagram which is the Jacobian Newton diagram of the morphism (f^(k),f), where f is a branch and f^(k) is a characteristic approximate root of f. We prove that the set of all approximate Jacobian Newton diagrams is a complete topological invariant. This generalizes theorems of Merle and Ephraim about the decomposition of the polar curve of a branch.