Einbettungen Steinscher Mannigfaltigkeiten
Let X be a Stein manifold of dimension n. A well-known conjecture in geometric function theory is the conjecture of Forster, namely that there exists an embedding of X in an affine space \({\mathbb{C}}^ N\) for \(N=n+1+[n/2]\). Forster has proved the existence of an embedding of X in \({\mathbb{C}}^ N\) for \(N=2n-[(n-2)/3]\) and \(n\geq 6\) [\textit{O. Forster}, Comm. Math. Helvet. 45, 170-184 (1970; Zbl 0184.314)]. In this paper an amelioration of Forster's result is given. For example, there exists an embedding of X in \({\mathbb{C}}^ N\) for \(N=2n-[2(n-5)/5]\) and \(n\geq 15\). Better bounds are given for greater n. Finally, it is proved that Forster's conjecture holds 'asymptotically'.
scientific article; zbMATH DE number 3865696