Oka properties of complements of holomorphically convex sets

• 成果类型: Article
• 署名作者: Kusakabe, Yuta
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2024.199.2.7
• 发表日期: 2024
• 页码: 899-917
• 关键词: stein-spaces; MAPS; approximation; AUTOMORPHISMS; EMBEDDINGS; MANIFOLDS; PRINCIPLE; THEOREM

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 Cn (n > 1) is Oka. Furthermore, we obtain new examples of non -elliptic 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 Cn \ R-k of a totally real affine subspace is Oka if n > 1 and (n, k) =6 (2, 1), (2, 2), (3, 3).