AI 中文总结
该研究针对亏格$g\geq2$的定向曲面稳定余切丛，构造了不可数多个互不同构且与$T^\ast\Sigma_g\times\mathbb{C}$ Stein形变等价的光滑仿射三维流形，其族由$(6g-7)$维复orbifold参数化，解答了Ivan Smith的问题。
AI 中文摘要
我们证明，对任意$g\geq2$，存在不可数多个互不同构的光滑仿射三维流形，它们与$T^\ast\Sigma_g\times\mathbb{C}$（亏格为$g$的定向曲面的余切丛与复平面的乘积）是Stein形变等价的，从而回答了Ivan Smith的一个问题。实际上，我们证明该光滑仿射三维流形族由一个$(6g-7)$维复orbifold参数化。
英文摘要
We show that for any $g\geq2$, there exist uncountably many non-isomorphic smooth affine threefolds that are Stein deformation equivalent to $T^\astΣ_g\times\mathbb{C}$, the product of the cotangent bundle of a genus $g$ oriented surface with the complex plane, answering a question of Ivan Smith. In fact, we prove that our family of smooth affine threefolds is parametrized by a $(6g-7)$-dimensional complex orbifold.
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