Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stability theorem for projective $CR$ manifolds   We consider smooth deformations of the $CR$ structure of a smooth
$2$-pseudoconcave compact $CR$ submanifold $\textsf{M}$ of a reduced complex
analytic variety $\textsf{X}$ outside the intersection $D\,{\cap}\,\textsf{M}$
with the support $D$ of a Cartier divisor of a positive line bundle
$\texttt{F}_{\textsf{X}}.$ We show that nearby structures still admit
projective $CR$ embeddings. Special results are obtained under the additional
assumptions that $\textsf{X}$ is a projective space or a Fano variety.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th