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Relative tangent cone of analytic curves. (English) Zbl 0966.32004

The author considers in her note irreducible germs of analytic curves \(X\), \(Y\) in the origin of \(\mathbb{C}^m\) and compares the tangent cones \(C_0(X)\), \(C_0(Y)\) with the relative tangent cone \(C_0(X,Y)\) to \(X\), \(Y\). The tangent cones are \(C_3\)-cones in the sense of Whitney. The author proves that \(C_0(X, Y)+ C_0(X)= C_0(X,Y)\), if \(X\cap Y= \{0\}\). She applies the result to counting the multiplicity of the intersection.

MSC:

32D10 Envelopes of holomorphy
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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