Memoirs of the American Mathematical Society 1997; 96 pp; softcover Volume: 125 ISBN10: 082180541X ISBN13: 9780821805411 List Price: US$46 Individual Members: US$27.60 Institutional Members: US$36.80 Order Code: MEMO/125/597
 In this memoir, it is shown that the parameter space for the versal deformation of an isolated singularity \((V,O)\) whose existence was established by Grauert in 1972is isomorphic to the space associated to the link \(M\) of \(V\) by Kuranishi using the CRgeometry of \(M\) . Readership Graduate students and research mathematicians interested in several complex variables and analytic spaces. Table of Contents  Introduction
 Controlling differential graded Lie algebras
 Vectorvalued differential forms on complex manifolds
 Kuranishi's CR deformation theory
 The global tangent complex of a complex analytic space
 The local tangent complex controls the flat deformations of an analytic local ring
 The global tangent complex controls the flat deformations of a complex analytic space
 The comparison of the tangent complex and the KodairaSpencer algebra of a complex manifold
 The Akahori complexes
 A controlling differential graded Lie algebra for Kuranishi's CRdeformation theory
 Counterexamples
 References
