Remote Access Proceedings of the American Mathematical Society
Green Open Access

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

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] M. Guisti and J. P. Henry, Minorations de nombres de Milnor, Bull. Soc. Math. France 108 (1980), 17-45. MR 603339 (82i:32034)
  • [2] G. M. Greuel, Der Gauss-Manin-Zusammenhang isolierter Singularitaten von vollstandigen 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] Le Dung Trang and C. P. Ramanujam, The invariance of Milnor's number implies the invariance of topological type, Amer. J. Math. 98 (1976), 67-78. MR 0399088 (53:2939)
  • [5] F. Pham, Remarques sur l'equisingularité universelle, preprint, Université de Nice, 1971. MR 1733363
  • [6] B. Teissier, The hunting of invariants in the geometry of discriminants, Real and Complex Singularities, Proceedings of the Nordic Summer School/NAVF, Oslo, 1976. MR 0568901 (58:27964)
  • [7] J. G. Timourian, The invariance of Milnor's number implies topological triviality, Amer. J. Math. 99 (1977), 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

Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society