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

Mihai Tibăr

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 411-419
  • ISSN: 0137-6934

Abstract

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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 ∈ . 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.

How to cite

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Tibăr, Mihai. "A supplement to the Iomdin-Lê theorem for singularities with one-dimensional singular locus." Banach Center Publications 33.1 (1996): 411-419. <http://eudml.org/doc/262734>.

@article{Tibăr1996,
abstract = {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 ∈ $. 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.},
author = {Tibăr, Mihai},
journal = {Banach Center Publications},
keywords = {polar curve; Milnor fibre},
language = {eng},
number = {1},
pages = {411-419},
title = {A supplement to the Iomdin-Lê theorem for singularities with one-dimensional singular locus},
url = {http://eudml.org/doc/262734},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Tibăr, Mihai
TI - A supplement to the Iomdin-Lê theorem for singularities with one-dimensional singular locus
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 411
EP - 419
AB - 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 ∈ $. 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.
LA - eng
KW - polar curve; Milnor fibre
UR - http://eudml.org/doc/262734
ER -

References

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  1. [Io] I. N. Iomdin, Variétés complexes avec singularités de dimension un, Sibirsk. Mat. Zh. 15 (1974), 1061-1082 (in Russian). 
  2. [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. 
  3. [Lê-2] D. T. Lê, The geometry of the monodromy theorem, in: C. P. Ramanujam--a Tribute, Tata Institute, Springer-Verlag 1978. 
  4. [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. 
  5. [Lê-4] D. T. Lê, Complex analytic functions with isolated singularities, J. Algebraic Geom., 1 (1992), 83-100. Zbl0777.32018
  6. [Si-1] D. Siersma, The monodromy of a series of hypersurface singularities, Comment. Math. Helv. 65 (1990), 181-197. Zbl0723.32015
  7. [Si-2] D. Siersma, Variation mappings on singularities with 1-dimensional singular locus, Topology 30 (1991), 445-469. Zbl0746.32014
  8. [Ti-1] M. Tibăr, Carrousel monodromy and Lefschetz number of singularities, Enseign. Math. 37 (1993), 233-247. Zbl0809.32010
  9. [Ti-2] M. Tibăr, Bouquet decomposition of the Milnor fibre, Topology 35 (1996), 227-242. Zbl0848.32031
  10. [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. Zbl0596.32014

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