The vanishing topology of non isolated singularities. (English) Zbl 1011.32021
Siersma, D. (ed.) et al., New developments in singularity theory. Proceedings of the NATO Advanced Study Institute on new developments in singularity theory, Cambridge, UK, July 31-August 11, 2000. Dordrecht: Kluwer Academic Publishers. NATO Sci. Ser. II, Math. Phys. Chem. 21, 447-472 (2001).
This paper is a survey of the work of author’s school on (non-isolated) singularities.
From the introduction: This paper is organized as follows. In section 2 we recall some facts about isolated singularities. In particular we discuss the relation between variation mapping, monodromy and intersection form.
In section 3 we treat singularities with a 1-dimensional critical set. We treat several examples, where vertical and horizontal monodromy play a role, and focus at the end on bouquet decompositions of the Milnor fibre. These seem to occur as soon as we stay near to the case of isolated singularities.
Section 4 is about singular sets of higher dimension. We discuss and summarize recent work.
For the entire collection see [Zbl 0968.00034].
From the introduction: This paper is organized as follows. In section 2 we recall some facts about isolated singularities. In particular we discuss the relation between variation mapping, monodromy and intersection form.
In section 3 we treat singularities with a 1-dimensional critical set. We treat several examples, where vertical and horizontal monodromy play a role, and focus at the end on bouquet decompositions of the Milnor fibre. These seem to occur as soon as we stay near to the case of isolated singularities.
Section 4 is about singular sets of higher dimension. We discuss and summarize recent work.
For the entire collection see [Zbl 0968.00034].
Reviewer: Daniel Barlet (Vandœuvre-les-Nancy)
MSC:
| 32S05 | Local complex singularities |
| 32S50 | Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants |
| 32S25 | Complex surface and hypersurface singularities |
