Series of Singularities and Their Topology

Abstract

This dissertation studies series of isolated singularities of plane curves. The focus is on topological properties. Important ingredients are the Eisenbud–Neumann diagrams and their splicing properties. We define the concept of topological series. We study Milnor numbers, monodromy and spectrum and describe a counter example to the spectrum conjecture The “roots” of the series are non-reduced plane curve singularties. We relate their topological properties with elements of the series. In the last sections we describe deformations of (non-reduced) plane curve singularities and also series of hypersurface singularities in general.