, Volume 32, Issue 1-2, pp 91-100

Puiseux expansion for space curves

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Abstract

For any ideal I in a convergent power series ring ℌ {X1,..,Xn} (n≥2) with one dimensional zero set X ⊂ (ℌn, 0) we give a method of computing a parametrization of each irreducible component of the reduction of X. This generalizes the well-known method of the Newton polygon or the so called Puiseux expansion for plane curves (see [N], [P], and [B]). The slope of a side of the Newton polygon is generalized to what we calltropism of the ideal. It may be visualized as the direction of a hyperplane touching the Newton polyhedron of every element of the ideal at least along an edge.

The author is grateful to the SFB 40 “Theoretische Mathematik”, Bonn, where this work was prepared.