The structure of a critical set of a complete intersection singularity

Yomdin, Yosef

doi:10.1090/S0002-9939-1982-0640237-9

The structure of a critical set of a complete intersection singularity
HTML articles powered by AMS MathViewer

by Yosef Yomdin PDF

Proc. Amer. Math. Soc. 84 (1982), 383-388 Request permission

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

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
G.-M. Greuel, Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 214 (1975), 235–266. MR 396554, DOI 10.1007/BF01352108

Calculation of the Milnor number of isolated singularity of complete intersection

8

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 399088, DOI 10.2307/2373614
Frédéric Pham, Le débat sur les “maths modernes”—est-il dépassé?, Gaz. Math. 81 (1999), 5–18 (French). MR 1733363
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
J. G. Timourian, The invariance of Milnor’s number implies topological triviality, Amer. J. Math. 99 (1977), no. 2, 437–446. MR 435444, DOI 10.2307/2373829

Euler characteristics of strata

for isolated singularities of complete intersections