发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Faculty of Mathematics, Kyushu University; State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院数学与系统科学研究院; 九州大学数学系; 中国科学院数学与系统科学研究院数学科学学院国家重点实验室; 中国科学院大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于Alpöge的环面纤维化构造复三维Oka族，研究其形变、切上同调、自同构群及双全纯等价条件，并利用循环覆盖与局部化原理证明Oka性质。
AI 中文摘要
从Alpöge在复六球面上具有恰好三个特殊纤维的环面纤维化出发，我们构造了一个局部极小万有的紧致复三维族。每个成员都是Oka的，且在每个相对紧的参数圆盘上的投影是Oka映射。删除或同时爆破有限多个不同点保持Oka性质。我们还确定了切上同调、光滑Kuranishi芽、自同构群以及精确的双全纯同构关系$X_a\simeq X_{a'}$当且仅当$a'-a\in2\mathbb{Z}$。Oka论证使用了显式循环覆盖和Kusakabe的局部化原理。
英文摘要
Starting from Alpöge's torus fibration with exactly three special fibres on a complex six-sphere, we construct a locally miniversal family of compact complex threefolds. Every member is Oka, and the projection over each relatively compact parameter disc is an Oka map. Deleting or simultaneously blowing up finitely many distinct points preserves the Oka property. We also determine the tangent cohomology, the smooth Kuranishi germ, the automorphism group, and the exact biholomorphism relation $X_a\simeq X_{a'}$ if and only if $a'-a\in2\mathbb{Z}$. The Oka arguments use explicit cyclic covers and Kusakabe's localization principle.
