Embeddings of Stein spaces into affine spaces of minimal dimension

Holomorphic flexibility properties of complex manifolds

“…An affine manifold is a closed complex or algebraic submanifold of a complex Euclidean space; an affine complex manifold is the same thing as a Stein manifold according to the embedding theorems [3], [18], [56], [59], [61].…”

Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

“…Concerning this dimension, Eliashberg, Gromov [11] and Schürmann [40] proved that any Stein manifold of dimension n > 1 can be embedded into C [3n/2]+1 . A key ingredient in these results is the homotopy principle for holomorphic sections of elliptic submersions over Stein manifolds [26], [18], [15].…”

“…These dimensions are the smallest possible due to an example of Forster [12]. The optimal dimension for embeddings of Stein spaces can be found in Schürmann's paper [40].…”

Embedding subsets of tori Properly into \mathbb{C}^2

“…A (finite) bordered Riemann surface is obtained by removing a finite set of closed disjoint connected components D 1 , ..., D k from a compact surface R, i.e., the bordered surface isR := R \ ∪ ] + 1 such that all Stein manifolds of dimension d embed properly into C N d [4], [5], [17] (for more details, see for instance the survey [8] For (positive) results when the genus of R is 0 we refer to the articles [14], [2], [15], [10], [20], and in the case of genus 1 to [7], [19].…”