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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finite jumps in Milnor number imply vanishing folds
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by Donal B. O’Shea PDF
Proc. Amer. Math. Soc. 87 (1983), 15-18 Request permission

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.
References
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 87 (1983), 15-18
  • MSC: Primary 14B07; Secondary 32B30, 32G11
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0677221-6
  • MathSciNet review: 677221