Algorithm for the Semigroup of a Space Curve Singularity |
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Authors: | Angel Castellanos Julio Castellanos |
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Institution: | (1) Dto. de Ciencias Basicas aplicadas, a la Ingenieria Forestal, Escuela Univ. de Ingenieria Tecnica, Forestal Universidad Politecnica de Madrid, Avda. de Ramiro de Maeztu s/n Madrid 28040 , Spain;(2) Departamento de Algebra, Facultad de Matematicas, Universidad Complutense, Madrid 28040 , Spain |
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Abstract: | The semigroup of values of irreducible space curve singularities
is the set of intersection multiplicities among hypersurfaces
and the given curve. It is an invariant of the singularity, and
for plane curves it characterizes the equisingularity type
considered by Zariski. For space curve singularities the semigroup
of values is a numerical semigroup and it can not be computed by
means of the exponents of any Puiseux parametrization, as in the
plane case. We obtain an algorithm for calculating the semigroup
of values of a space curve singularity, which determines the
generators of the semigroup and the valuation ideals associated
with the semigroup. We give a Maple version of the algorithm. |
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Keywords: | |
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