Unfolding CR singularities / Adam Coffman.

Format:

Book

Author/Creator:

Coffman, Adam, 1971- author.

Series:

Memoirs of the American Mathematical Society ; Volume 205, Number 962.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 205, Number 962

Language:

English

Subjects (All):

CR submanifolds.

Deformations of singularities.

Global analysis (Mathematics).

Physical Description:

1 online resource (90 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2009.

Language Note:

English

Summary:

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. Table of Contents: Introduction; Topological considerations; Local defining equations and transformations; A complexification construction; Real surfaces in $\mathbb{C} DEGREES2$; Real $m$-submanifolds in $\mathbb{C} DEGREESn, m

Contents:

""Contents""; ""Abstract""; ""List of Figures""; ""Unfolding CR singularities""; ""1. Introduction""; ""2. Topological considerations""; ""2.1. A grassmannian construction""; ""2.2. Global index sums""; ""3. Local defining equations and transformations""; ""3.1. Defining equations for m-submanifolds in Cn""; ""3.2. Parametrized families of submanifolds""; ""3.3. The transformation group for unfoldings""; ""4. A complexification construction""; ""5. Real surfaces in C2""; ""5.1. Normal forms""; ""5.2. Unfolding CR singularities of surfaces""; ""5.3. Visualization""

""6. Real m-submanifolds in Cn, m<n""""6.1. Normal forms""; ""6.2. Unfolding CR singularities of m-submanifolds""; ""6.3. The geometry of the algebraic unfolding""; ""7. Rapid convergence proof of the main theorem""; ""7.1. A functional equation""; ""7.2. A solution of a linearized equation""; ""7.3. The new defining equations and some estimates""; ""7.4. Composition of approximate solutions""; ""8. Some other directions""; ""Bibliography""

Notes:

"Volume 205, Number 962 (first of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0576-8