## 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

### Keywords:

analytic curves; tangent cones
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