manuscripta mathematica

, Volume 32, Issue 1, pp 91–100

Puiseux expansion for space curves

  • Joseph Maurer

DOI: 10.1007/BF01298184

Cite this article as:
Maurer, J. Manuscripta Math (1980) 32: 91. doi:10.1007/BF01298184


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.

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Joseph Maurer
    • 1
  1. 1.Mathematisches InstitutUniversität DüsseldorfDüsseldorfFederal Republic of Germany

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