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Finite jumps in Milnor number imply vanishing folds

Author: Donal B. O’Shea
Journal: Proc. Amer. Math. Soc. 87 (1983), 15-18
MSC: Primary 14B07; Secondary 32B30, 32G11
MathSciNet review: 677221
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Abstract: Let $ \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}$ at which the Milnor number of the $ {X_t}$ changes discontinuously. This is much stronger than the condition that the Whitney conditions fail.

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Article copyright: © Copyright 1983 American Mathematical Society