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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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