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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
CR-Geometry and Deformations of Isolated Singularities
eBook 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
CR-Geometry and Deformations of Isolated Singularities
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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
eBook 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 \(M\) .

    Readership

    Graduate 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. 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 publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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 \(M\) .

Readership

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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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