Unfolding CR singularities
article 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.