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 Memoirs of the American Mathematical Society
Memoirs of the American Mathematical Society
ISSN 1947-6221(e) ISSN 0065-9266(p)

     

Unfolding CR Singularities

Author(s): Adam Coffman
Journal: Memoirs of the AMS 205 (2010), no. 962.
MSC (2000): Primary 32V40, 32S30, 58K35
Posted: December 1, 2009
MathSciNet review: 2650710
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: A notion of unfolding, or multi-parameter deformation, of CR singularities of real submanifolds in complex manifolds is proposed, along with a definition of equivalence of unfoldings under the action of a group of analytic transformations. In the case of real surfaces in complex $ 2$-space, deformations of elliptic, hyperbolic, and parabolic points are analyzed by putting the parameter-dependent real analytic defining equations into normal forms up to some order. For some real analytic unfoldings in higher codimension, the method of rapid convergence is used to establish real algebraic normal forms.

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Additional Information:

Adam Coffman
Affiliation: Department of Mathematical Sciences, Indiana University - Purdue University Fort Wayne, 2101 E. Coliseum Blvd., Fort Wayne, Indiana 46805-1499
Email: CoffmanA@ipfw.edu

DOI: 10.1090/S0065-9266-09-00575-4
PII: S 0065-9266(09)00575-4
Keywords: CR singularity, normal form, real submanifold
Received by editor(s): August 8, 2006
Posted: December 1, 2009
Additional Notes: Presented to the American Mathematical Society at the Spring 2006 Central Section Meeting.
Affiliation at time of publication: Department of Mathematical Sciences, Indiana University - Purdue University Fort Wayne, 2101 E. Coliseum Blvd., Fort Wayne, IN 46805-1499; email:CoffmanA@ipfw.edu.
Copyright of article: Copyright 2009, American Mathematical Society




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