Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The structure of a critical set of a complete intersection singularity

Author: Yosef Yomdin
Journal: Proc. Amer. Math. Soc. 84 (1982), 383-388
MSC: Primary 32B30; Secondary 14B05
MathSciNet review: 640237
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f:({C^n},0) \to ({C^k},0)$ be the germ of an isolated complete intersection singularity. The structure of strata $ \mu = \operatorname{const} $ in a critical set of $ f$ is studied. The main result is the following: if the dimension of the stratum $ \mu = \mu (0)$ is $ k - 1$, then $ f$ coincides with a family of hypersurface singularities with constant Milnor number.

References [Enhancements On Off] (What's this?)

  • [1] Marc Giusti and Jean-Pierre-Georges Henry, Minorations de nombres de Milnor, Bull. Soc. Math. France 108 (1980), no. 1, 17–45 (French, with English summary). MR 603339 (82i:32034)
  • [2] G.-M. Greuel, Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 214 (1975), 235–266. MR 0396554 (53 #417)
  • [3] Le Dung Trang, Calculation of the Milnor number of isolated singularity of complete intersection, Functional Anal. Appl. 8 ( 1974), 127-131.
  • [4] Lê Dũng Tráng and C. P. Ramanujam, The invariance of Milnor’s number implies the invariance of the topological type, Amer. J. Math. 98 (1976), no. 1, 67–78. MR 0399088 (53 #2939)
  • [5] Frédéric Pham, Le débat sur les “maths modernes”—est-il dépassé?, Gaz. Math. 81 (1999), 5–18 (French). MR 1733363
  • [6] Bernard Teissier, The hunting of invariants in the geometry of discriminants, Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 565–678. MR 0568901 (58 #27964)
  • [7] J. G. Timourian, The invariance of Milnor’s number implies topological triviality, Amer. J. Math. 99 (1977), no. 2, 437–446. MR 0435444 (55 #8404)
  • [8] Y. Yomdin, Euler characteristics of strata $ \mu = \operatorname{const} $ for isolated singularities of complete intersections, preprint, Ben Gurion University of the Negev, 1979.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32B30, 14B05

Retrieve articles in all journals with MSC: 32B30, 14B05

Additional Information

PII: S 0002-9939(1982)0640237-9
Article copyright: © Copyright 1982 American Mathematical Society