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. Moreover we study the singularity at infinity of a plane affine curve with one point at infinity for which the global counterpart of our main result holds.

References in corpus (1)

• Jacobian Newton Polyhedra and equisingularity

Cited by in corpus (5)

• Quasi-ordinary singularities: tree model, discriminant and irreducibility
• On the approximate jacobian Newton diagrams of an irreducible plane curve
• A quasi-linear irreducibility test in K[[x]][y]
• Topological type of discriminants of some special families
• Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]