全纯凸集补集的Oka性质
Oka properties of complements of holomorphically convex sets
AI总结：
本文证明具有密度性质的Stein流形中紧全纯凸集的补集是Oka流形，肯定回答了Oka理论中的长期问题，并给出非椭圆Oka流形的新例子否定回答Gromov问题。
摘要：
我们的主要定理指出，具有密度性质的Stein流形中紧全纯凸集的补集是Oka流形。这肯定回答了Oka理论中长期著名的问题，即$\mathbb{C}^{n}$ $(n>1)$中紧多项式凸集的补集是否为Oka。此外，我们获得了非椭圆Oka流形的新例子，否定回答了Gromov的问题。还证明了主要定理的相对版本。作为应用，我们证明当$n>1$且$(n,k)\neq(2,1),(2,2),(3,3)$时，全实仿射子空间的补集$\mathbb{C}^{n}\setminus\mathbb{R}^{k}$是Oka。
英文摘要：
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 $(n,k)\neq(2,1),(2,2),(3,3)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
