Distinguished bases and monodromy of complex hypersurface singularities

Abstract

We give a survey on some aspects of the topological investigation of isolated singularities of complex hypersurfaces by means of Picard-Lefschetz theory. We focus on the concept of distinguished bases of vanishing cycles and the concept of monodromy. ContentsIntroduction 1 1. Distinguished bases of vanishing cycles 3 2. Coxeter-Dynkin diagram and Seifert form 11 3. Change of basis 13 4. Computation of intersection matrices 18 5. The discriminant and the Lyashko-Looijenga map 21 6. Special singularities 24 7. The monodromy group 31 8. Topological equivalence 35 References 37 Index 46