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.
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[M] MACMILLAN, W. D.: A method for determining the solutions of a system of analytic functions in the neighborhood of a branch point. Math. Ann.72 (1912) 180–202
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The author is grateful to the SFB 40 “Theoretische Mathematik”, Bonn, where this work was prepared.
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Maurer, J. Puiseux expansion for space curves. Manuscripta Math 32, 91–100 (1980). https://doi.org/10.1007/BF01298184
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DOI: https://doi.org/10.1007/BF01298184