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Unfolding CR Singularities
About this Title
Adam Coffman, Department of Mathematical Sciences, Indiana University - Purdue University Fort Wayne, 2101 E. Coliseum Blvd., Fort Wayne, Indiana 46805-1499
Publication: Memoirs of the American Mathematical Society
Publication Year:
2010; Volume 205, Number 962
ISBNs: 978-0-8218-4657-5 (print); 978-1-4704-0576-2 (online)
DOI: https://doi.org/10.1090/S0065-9266-09-00575-4
Published electronically: December 1, 2009
Keywords: CR singularity,
normal form,
real submanifold
MSC: Primary 32V40, 32S30, 58K35
Table of Contents
Chapters
- Unfolding CR singularities
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.- Lars V. Ahlfors, Complex analysis, 3rd ed., International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., New York, 1978. An introduction to the theory of analytic functions of one complex variable. MR 510197
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