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A.4.7 Branches of space curve singularities

In this example, the number of branches of a given quasihomogeneous isolated space curve singularity will be computed as an example of the pitfalls appearing in the use of primary decomposition. When dealing with singularities, two situations are possible in which the primary decomposition algorithm might not lead to a complete decomposition: first of all, one of the computed components could be globally irreducible, but analytically reducible (this is impossible for quasihomogeneous singularities) and, as a second possibility, a component might be irreducible over the rational numbers, but reducible over the complex numbers.
 


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