μ-constant monodromy groups and Torelli results for marked singularities, for the unimodal and some bimodal singularities

2015/11/27 by Falko Gauß, Gauss, Falko, Claus Hertling +1
Mathematics · #14D22 #32S15 #32S40 #58K70 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1511.08660

openalex publication_date 2015/11/27 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

This paper is a sequel to [He7]. 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⊂ G_Z. Here G_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_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.

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