A supplement to the Iomdin-Lê theorem for singularities with one-dimensional singular locus

• Autorzy: Mihai Tibăr
• Języki publikacji: EN

Abstrakty

EN

To a germ $f: (ℂ^n,0) → (ℂ,0)$ with one-dimensional singular locus one associates series of isolated singularities $f_N := f + l^N$, where l is a general linear function and $N ∈ 𝔹$. We prove an attaching result of Iomdin-Lê type which compares the homotopy types of the Milnor fibres of $f_N$ and f. This is a refinement of the Iomdin-Lê theorem in the general setting of a singular underlying space.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 411-419

Daty

wydano

1996

Twórcy

autor

Mihai Tibăr

• Département de Mathéematiques, Université d'Angers, 2, bd. Lavoisier, 49045 Angers Cedex 01, France

Bibliografia

• [Io] I. N. Iomdin, Variétés complexes avec singularités de dimension un, Sibirsk. Mat. Zh. 15 (1974), 1061-1082 (in Russian).
• [Lê-1] D. T. Lê, Ensembles analytiques avec lieu singulier de dimension 1 (d'après Iomdine), in: Séminaire sur les singularités, Publ. Math. de l'Université Paris VII, 1980, 87-95.
• [Lê-2] D. T. Lê, The geometry of the monodromy theorem, in: C. P. Ramanujam--a Tribute, Tata Institute, Springer-Verlag 1978.
• [Lê-3] D. T. Lê, Some remarks on the relative monodromy, in: Real and Complex Singularities Oslo 1976, Sijthoff en Noordhoff, Alphen a.d. Rijn 1977, 397-403.
• [Lê-4] D. T. Lê, Complex analytic functions with isolated singularities, J. Algebraic Geom., 1 (1992), 83-100.
• [Si-1] D. Siersma, The monodromy of a series of hypersurface singularities, Comment. Math. Helv. 65 (1990), 181-197.
• [Si-2] D. Siersma, Variation mappings on singularities with 1-dimensional singular locus, Topology 30 (1991), 445-469.
• [Ti-1] M. Tibăr, Carrousel monodromy and Lefschetz number of singularities, Enseign. Math. 37 (1993), 233-247.
• [Ti-2] M. Tibăr, Bouquet decomposition of the Milnor fibre, Topology 35 (1996), 227-242.
• [Va] J.-P. Vannier, Familles à un paramètre de fonctions analytiques à lieu singulier de dimension un, C. R. Acad. Sci. Paris Sér. I 303 (1986), 367-370.