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The jump of the Milnor number in the $$X_9$$ singularity class. (English) Zbl 1286.32014
Summary: The jump of the Milnor number of an isolated singularity $$f_0$$ is the minimal non-zero difference between the Milnor numbers of $$f_0$$ and one of its deformations $$(f_s)$$. We prove that for the singularities in the $$X_9$$ singularity class their jumps are equal to 2.

##### MSC:
 32S05 Local complex singularities 32S10 Invariants of analytic local rings 14B05 Singularities in algebraic geometry 14B07 Deformations of singularities
##### Keywords:
Milnor number; singularity; deformation of singularity
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##### References:
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