Geometry near a C.R. singularity

This paper is concerned with the local geometry of a real-analytic submanifold of C in the vicinity of a C.R. singular point. The concept of local generic embeddability near a C.R. singularity is introduced in Section 1. Unlike the C.R. situation, not all non-C.R, real-analytic submanifolds of C are locally generically embeddable. Hence a new concept, pseudo-generic embeddability, is developed. The section concludes with a description of generic embeddability in the context of the theory of analytic local rings. Unfortunately this description is in terms of some dimensions which are not generally computable by known methods. Therefore the emphasis of this paper is Sections 2 and 3 where a simple scheme is developed to study these concepts for two-dimensional real-analytic submanifolds of Ca.