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CR-Geometry and Deformations of Isolated Singularities

Ragnar-Olaf Buchweitz University of Toronto, Toronto, ON, Canada
John J. Millson University of Maryland, College Park, MD
Available Formats:
Electronic ISBN: 978-1-4704-0182-5
Product Code: MEMO/125/597.E
List Price: $46.00 MAA Member Price:$41.40
AMS Member Price: $27.60 Click above image for expanded view CR-Geometry and Deformations of Isolated Singularities Ragnar-Olaf Buchweitz University of Toronto, Toronto, ON, Canada John J. Millson University of Maryland, College Park, MD Available Formats:  Electronic ISBN: 978-1-4704-0182-5 Product Code: MEMO/125/597.E  List Price:$46.00 MAA Member Price: $41.40 AMS Member Price:$27.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1251997; 96 pp
MSC: 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 CR-geometry 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. Vector-valued 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 Kodaira-Spencer algebra of a complex manifold
• 8. The Akahori complexes
• 9. A controlling differential graded Lie algebra for Kuranishi’s CR-deformation theory
• 10. Counterexamples
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 1251997; 96 pp
MSC: 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 CR-geometry 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. Vector-valued 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 Kodaira-Spencer algebra of a complex manifold
• 8. The Akahori complexes
• 9. A controlling differential graded Lie algebra for Kuranishi’s CR-deformation theory
• 10. Counterexamples
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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