On realizations of families of strongly pseudo-convex CR structures (Q1201468)

Let \((V,0)\) be a normal isolated singularity and \(M\) its link. The author proved in a previous paper that, if \(\dim_ c (V,0) \geq 4\) and \(\text{depth} (V,0)>3\), then the Kuranishi family of CR structures on \(M\) induces the versal family of \((V,0)\). Here, he proves, for a strongly pseudoconvex real hypersurface of a complex manifold \(X\) with \(\dim_ c X \geq 4\), any versal family of CR structures on \(M\) in the sense of Kuranishi is realized as a real hypersurface of the versal family of deformations of \(X\) near \(M\) and that, in particular, their parametric spaces coincides with each other.