论文标题
Holomororthally凸面集的补充的OKA属性
Oka properties of complements of holomorphically convex sets
论文作者
论文摘要
我们的主要定理指出，与密度属性的Stein歧管中的紧凑型全态凸的补充是OKA歧管。这给出了OKA理论中众所周知的长期问题的积极答案，是否在$ \ Mathbb {C}^{n} $ $（n> 1）$的紧凑多项式凸的补充是否为Oka。此外，我们获得了非戏剧性OKA流形的新例子，这些示例对Gromov的问题负面回答。还证明了主要定理的相对版本。作为一个应用程序，我们证明了一个完全真实的Aggine子空间为OKA的补体$ \ Mathbb {C}^{n} \ setMinus \ Mathbb {r}^{k} $，如果$ n> 1 $和$ n> 1 $和$（n，k）
Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold. This gives a positive answer to the well-known long-standing problem in Oka theory whether the complement of a compact polynomially convex set in $\mathbb{C}^{n}$ $(n>1)$ is Oka. Furthermore, we obtain new examples of nonelliptic Oka manifolds which negatively answer Gromov's question. The relative version of the main theorem is also proved. As an application, we show that the complement $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$ of a totally real affine subspace is Oka if $n>1$ and $(n,k)\neq(2,1),(2,2),(3,3)$.
