The McKay correspondence and resolving the Kleinian singularities

Abstract

In this thesis we find and blow up the Kleinian singularities and show their relationship with Dynkin diagrams of type ADE. Furthermore, we construct the McKay graphs of the finite subgroups of SL(2,C) and show their connection with the ADE type Dynkin diagrams and hence the Kleinian singularities. The purpose of this thesis is to establish all of the above in great detail and to work out the specifics.