Local Theory of Several Complex Variables

Abstract

We want to study the quotient varieties (ℂ2 /G of the finite subgroups of SL(2, ℂ) and their singularities from the viewpoint of complex analytic geometry. Further, we like to show how they fit into the general context of singularities. This requires some knowledge of complex analysis of several variables. This chapter does not present a full discussion of the topic. It is rather a concise introduction which covers the general background as well as special results for later use. Since ‘very local’ results will suffice, no coherent sheaves will occur.