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 \({{\mathbb {C}}}^m\) ${\mathbb{C}}^m$ for some \(m<\infty \) $m<\infty$ when \((TM)|_C\) ${(TM)|}_C$ is fixed and the normal bundle of C in M is either weakly negative or 2-positive.