六球面的条件Oka复结构
Conditional Oka Complex Structures of the Six-Sphere
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中文总结 AI 辅助
本文证明Alpöge构造的紧致复三维流形$Y$是Oka流形，从而在特定条件下赋予六球面$S^6$一个Oka复结构，且该证明不依赖拓扑等同。
中文摘要 AI 辅助
Alpöge构造了一个紧致复三维流形$Y$，它通过复二维环面在$\nmathbb{P}^1$上纤维化，且远离三个特殊点。我们证明$Y$是一个Oka流形。该证明适用于所有具有相同对数扭曲和尖点粘合的容许周期参数。若同时接受Alpöge定理8.1中底层光滑流形与$S^6$的等同，则六球面具有Oka复结构。此拓扑等同在Oka证明中未被使用。
英文摘要
Alpöge's construction produces a period family of compact complex threefolds fibred over $\mathbb{P}^1$, with complex two-tori as general fibres. We give a direct proof that every admissible member is Oka, using only the complex-analytic construction. Du--Guo--Kusakabe--Xie independently established the Oka property and determined the exact biholomorphism classes in this family. Assuming Alpöge's identification of the underlying smooth manifolds with $S^6$, these results yield uncountably many pairwise nonbiholomorphic Oka complex structures on the six-sphere.
发表机构
- East China Normal University（华东师范大学）
机构由 AI 辅助整理，请以论文原文为准。
