Applications

Abstract

In this chapter we apply the results and methods from the previous two chapters to a variety of problems on Stein spaces. We discuss the structure of holomorphic vector bundles and their homomorphisms over Stein spaces, find the minimal number of generators of a coherent analytic sheaf, consider the problem of complete intersections and of elimination of intersections of holomorphic maps with complex subvarieties, present the solution of the holomorphic Vaserstein problem, discuss transversality theorems for holomorphic and algebraic maps from Stein manifolds, and prove a Runge type approximation theorem for algebraic maps from affine algebraic varieties to a certain class of algebraic manifolds.