Most real analytic Cauchy-Riemann manifolds are nonalgebraizable

We give a simple argument to the effect that most germs of generic real analytic Cauchy-Riemann manifolds of positive CR dimension are not holomorphically embeddable into a generic real algebraic CR manifold of the same real codimension in a finite dimensional space. In particular, most such germs are not holomorphically equivalent to a germ of a generic real algebraic CR manifold.Mathematics Subject Classification (2000): Primary 32V20, 32V30Supported in part by Research Program P1-0291, Republic of SloveniaAcknowledgement I wish to thank Peter Ebenfelt and Alexander Sukhov for their invaluable advice concerning the state of knowledge on the question considered in the paper.