A structure theorem for neighborhoods of compact complex manifolds

We construct an injective map from the set of holomorphic equivalence classes of neighborhoods $M$ of a compact complex manifold $C$ into ${\mathbb{C}}^m$ for some $m<\mathrm{\infty }$ when $(TM){\mathrm{\mid }}_C$ is fixed and the normal bundle of $C$ in $M$ is either weakly negative or $2$-positive.