Definition 5.2.342A02A1A5EFE

Definition 5.2.3.42A02A1A5EFE A complex manifold of dimension $n$ is a paracompact Hausdorff space with an atlas of homeomorphisms onto open subsets of $\mathbb {C}^ n$, whose coordinate changes are holomorphic with holomorphic inverses. A map between complex manifolds is holomorphic if its coordinate expressions are holomorphic. A complex submanifold is a closed subset that is locally a coordinate plane in suitable holomorphic coordinates.