ABSTRACT
We consider smooth deformations of the CR structure of a smooth 2-pseudoconcave compact CR submanifold of a reduced complex analytic variety
outside the intersection
with the support D of a Cartier divisor of a positive line bundle
We show that nearby structures still admit projective CR embeddings. Special results are obtained under the additional assumptions that
is a projective space or a Fano variety.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 We recall that, if is a vector space, the monomials of degree
of its exterior algebra
are the exterior products
of vectors
of
2 This is obtained by identifying with its vertical bundle and first defining
on the smooth local sections s of
by setting
In fact, when s is a section, the right-hand side of () is vertical.
3 A real valued smooth function ϕ on an -dimensional complex manifold
is strongly
-pseudoconvex in the sense of [Citation29] at points where its complex Hessian has at least
positive eigenvalues. Then
is called strictly
-pseudoconvex if there is an exhaustion function
which is strictly
-pseudoconvex outside a compact subset of
and strictly
-pseudoconcave if there is an exhaustion function
such that
is strictly
-pseudoconvex outside a compact subset of