A **Stein manifold** is a concept from complex geometry which refers to a particular class of complex manifolds that generalize certain properties of complex affine varieties. Stein manifolds are considered the complex-analytic counterpart of affine algebraic varieties.
Articles by others on the same topic
A complex manifold is Stein if its global holomorphic functions separate points, give local coordinates, and make it holomorphically convex: the holomorphic hull of every compact set is compact. Closed complex submanifolds of affine complex space are examples, including products of copies of and . Cartan theorem B makes these spaces useful for acyclic covers in sheaf cohomology.