Deformations of Singularities, Complex Manifolds and CR-Structures

Abstract

This note is an expanded version of the author’s lecture at the conference on Several Complex Variables held in Osaka, Dec. 1994. We consider deformations of complex spaces and their relationship to deformations of CR-structures. An invariant is introduced which measures the change in the algebra of CR-functions under a deformation. These issues are then considered in the context of the deformations of the total space of the tangent bundle of a Riemann surface. The last section contains problems in deformation theory.