A stability theorem for projective $CR$ manifolds

Abstract

We consider smooth deformations of the $CR$ structure of a smooth $2$-pseudoconcave compact $CR$ submanifold $\text{M}$ of a reduced complex analytic variety $\text{X}$ outside the intersection $D\cap \text{M}$ with the support $D$ of a Cartier divisor of a positive line bundle ${\text{F}}_{\text{X}}.$ We show that nearby structures still admit projective $CR$ embeddings. Special results are obtained under the additional assumptions that $\text{X}$ is a projective space or a Fano variety.

minor corrections