μ-Constant Monodromy Groups and Torelli Results for Marked Singularities, for the Unimodal and Some Bimodal Singularities

This paper is a sequel to Hertling (Ann Inst Fourier (Grenoble) 61(7):2643–2680, 2011). There a notion of marking of isolated hypersurface singularities was defined, and a moduli space M μ mar for marked singularities in one μ-homotopy class of isolated hypersurface singularities was established. One can consider it as a global μ-constant stratum or as a Teichmüller space for singularities. It comes together with a μ-constant monodromy group $$G^{mar} \subset G_{\mathbb{Z}}$$ . Here $$G_{\mathbb{Z}}$$ is the group of automorphisms of a Milnor lattice which respect the Seifert form. It was conjectured that M μ mar is connected. This is equivalent to $$G^{mar} = G_{\mathbb{Z}}$$ . Also Torelli-type conjectures were formulated. All conjectures were proved for the simple singularities and 22 of the exceptional unimodal and bimodal singularities. In this paper, the conjectures are proved for the remaining unimodal singularities and the remaining exceptional bimodal singularities.