We construct closed complex submanifolds of ${ℂ}^n$ which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of ${ℂ}^n$.

In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold $X$, with 1- dimensional exceptional set $S$ and finitely generated second homology group $H_2(X,\mathbb{Z})$, is embeddable in ${ℂ}^m\times ℂ{\mathbb{P}}_n$ if and only if $X$ is Kähler, and this case occurs only when $S$ does not contain any effective curve which is a boundary.