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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
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