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Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility

Evelia R. García Barroso;  Janusz Gwoździewicz — 2010

Annales de l’institut Fourier

In this paper we characterize, in two different ways, the Newton polygons which are jacobian Newton polygons of a plane branch. These characterizations give in particular combinatorial criteria of irreducibility for complex series in two variables and necessary conditions which a complex curve has to satisfy in order to be the discriminant of a complex plane branch.

Pinceaux de courbes planes et invariants polaires

Evelia R. García Barroso;  Arkadiusz Płoski — 2004

Annales Polonici Mathematici

We study pencils of plane curves f t = f - t l N , t ∈ ℂ, using the notion of polar invariant of the plane curve f = 0 with respect to a smooth curve l = 0. More precisely we compute the jacobian Newton polygon of the generic fiber f t , t ∈ ℂ. The main result gives the description of pencils which have an irreducible fiber. Furthermore we prove some applications of the local properties of pencils to singularities at infinity of polynomials in two complex variables.

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