Stein space

Summary

A Stein space is a complex analytic space with enough global holomorphic functions: they separate points and give compact holomorphically convex hulls of compact sets. It extends the notion of Stein manifold to spaces with singularities, as affine schemes extend affine varieties. Stein spaces are exactly the complex spaces on which every coherent analytic sheaf has vanishing higher cohomology. Closed complex subspaces of $\C^N$ are the main examples.