Most real analytic Cauchy-Riemann manifolds are nonalgebraizable

Details Most real analytic Cauchy-Riemann manifolds are nonalgebraizable Most real analytic Cauchy-Riemann manifolds are nonalgebraizable

2004-06-10

arxiv.org/abs/math/0406210v2

Manuscripta math., 115 (2004), 489-494

Mathematics

Complex Variables

To appear in Manuscripta Math

Scientific paper

10.1007/s00229-004-0507-4

We give a very simple argument to the effect that most germs of generic real analytic Cauchy-Riemann manifolds of positive CR dimension are not holomorphically embeddable into any 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.

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