A discriminant criterion of irreducibility

Abstract

In this paper we give a criterion of irreducibility for a complex power series in two variables, using the notion of jacobian Newton diagrams, defined with respect to any direction. Then we apply our method to study the branches of plane algebraic curves. For an affine plane curve with one point at infinity, we also obtain a criterion for an analytical irreducibility in terms of the Newton diagram of a discriminant, without using coordinates centered at the point at infinity.