Electronic ISBN:  9781470401825 
Product Code:  MEMO/125/597.E 
List Price:  $46.00 
MAA Member Price:  $41.40 
AMS Member Price:  $27.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 125; 1997; 96 ppMSC: Primary 32; 14;
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 1972—is isomorphic to the space associated to the link \(M\) of \(V\) by Kuranishi using the CRgeometry of \(M\) .
ReadershipGraduate students and research mathematicians interested in several complex variables and analytic spaces.

Table of Contents

Chapters

0. Introduction

1. Controlling differential graded Lie algebras

2. Vectorvalued differential forms on complex manifolds

3. Kuranishi’s CR deformation theory

4. The global tangent complex of a complex analytic space

5. The local tangent complex controls the flat deformations of an analytic local ring

6. The global tangent complex controls the flat deformations of a complex analytic space

7. The comparison of the tangent complex and the KodairaSpencer algebra of a complex manifold

8. The Akahori complexes

9. A controlling differential graded Lie algebra for Kuranishi’s CRdeformation theory

10. Counterexamples


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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 1972—is isomorphic to the space associated to the link \(M\) of \(V\) by Kuranishi using the CRgeometry of \(M\) .
Graduate students and research mathematicians interested in several complex variables and analytic spaces.

Chapters

0. Introduction

1. Controlling differential graded Lie algebras

2. Vectorvalued differential forms on complex manifolds

3. Kuranishi’s CR deformation theory

4. The global tangent complex of a complex analytic space

5. The local tangent complex controls the flat deformations of an analytic local ring

6. The global tangent complex controls the flat deformations of a complex analytic space

7. The comparison of the tangent complex and the KodairaSpencer algebra of a complex manifold

8. The Akahori complexes

9. A controlling differential graded Lie algebra for Kuranishi’s CRdeformation theory

10. Counterexamples