A structure theorem for neighborhoods of compact complex manifolds

TL;DR

This paper establishes a structure theorem for neighborhoods of compact complex manifolds, providing an injective map into complex Euclidean space under certain positivity conditions on the normal bundle.

Contribution

It introduces a new structure theorem that characterizes neighborhoods of compact complex manifolds via an injective map into complex Euclidean space, given specific bundle conditions.

Findings

Injective map from neighborhoods to ^m for some m

Applicable when the normal bundle is weakly negative or 2-positive

Provides a classification framework for neighborhoods of complex manifolds

Abstract

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