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arXiv · 2610.00250

Oka Geometry and Deformations of Torus-Fibred Complex Six-Spheres

Yun-Heng Du·Bin Guo·Yuta Kusakabe·Song-Yan Xie
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Abstract

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.

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Yun-Heng Du, Bin Guo, Yuta Kusakabe, Song-Yan Xie. 2026-09-23. Oka Geometry and Deformations of Torus-Fibred Complex Six-Spheres. https://arxiv.org/abs/2610.00250

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