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CR-Geometry and Deformations of Isolated Singularities
Ragnar-Olaf Buchweitz, University of Toronto, ON, Canada, and John J. Millson, University of Maryland, College Park, MD
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Memoirs of the American Mathematical Society
1997; 96 pp; softcover
Volume: 125
ISBN-10: 0-8218-0541-X
ISBN-13: 978-0-8218-0541-1
List Price: US$46
Individual Members: US$27.60
Institutional Members: US$36.80
Order Code: MEMO/125/597
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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 CR-geometry 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
  • Vector-valued 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 Kodaira-Spencer algebra of a complex manifold
  • The Akahori complexes
  • A controlling differential graded Lie algebra for Kuranishi's CR-deformation theory
  • Counterexamples
  • References
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