Desingularization of ADE Singularities via Deformation

The topology and structure of the ADE singularities in terms of their topological invariants are recalled. A representation of these curves as Riemann surfaces is used to propose a novel technique of visualization of multivalued complex functions. Here, not only the entire domain is displayed, but also the method of domain coloring is extended via utilizing a specific height function. The method is applied in order to show the structure of singularities and to resolve them. A sequence of 1-parameter deformations is used, each causing Milnor number to drop by one up to regularity. The changes in the internal structure are interpreted and the whole process is visualized via computer animation.