Finite Jumps in Milnor Number Imply Vanishing Folds
Copyright policy )Finite Jumps in Milnor Number Imply Vanishing Folds
Let { X t } \left \{ {{X_t}} \right \} be a family of isolated hypersurface singularities in which the Milnor number is not constant. It is proved that there must be a vanishing fold centered at any t = t 0 t = {t_0} at which the Milnor number of the X t {X_t} changes discontinuously. This is much stronger than the condition that the Whitney conditions fail.
Deformations of complex singularities; vanishing cycles, Local complex singularities, Deformations of singularities, Structure of families (Picard-Lefschetz, monodromy, etc.), families of complex hypersurfaces with isolated singularity, Families, moduli, classification: algebraic theory, Complex singularities, jumps in Milnor number, Singularities of surfaces or higher-dimensional varieties, Singularities of differentiable mappings in differential topology
Deformations of complex singularities; vanishing cycles, Local complex singularities, Deformations of singularities, Structure of families (Picard-Lefschetz, monodromy, etc.), families of complex hypersurfaces with isolated singularity, Families, moduli, classification: algebraic theory, Complex singularities, jumps in Milnor number, Singularities of surfaces or higher-dimensional varieties, Singularities of differentiable mappings in differential topology
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