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arXiv · 2608.30440

Abundance of affine algebraic structures on stabilized cotangent bundles of surfaces

Yin Li
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Abstract

We show that for any $g\geq2$, there exist uncountably many non-isomorphic smooth affine threefolds that are Stein deformation equivalent to $T^\ast\Sigma_g\times\mathbb{C}$, 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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BibTeXRIS

Yin Li. 2026-08-31. Abundance of affine algebraic structures on stabilized cotangent bundles of surfaces. https://arxiv.org/abs/2608.30440

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