PreprintCC BY 4.0arXiv
Abundance of affine algebraic structures on stabilized cotangent bundles of surfaces
Abstract
We show that for any g≥2, there exist uncountably many non-isomorphic smooth affine threefolds that are Stein deformation equivalent to T∗Σg×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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BibTeX
@misc{li2026abundance,
title = {{Abundance of affine algebraic structures on stabilized cotangent bundles of surfaces}},
author = {Yin Li},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30440},
eprint = {2608.30440},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30440},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Abundance of affine algebraic structures on stabilized cotangent bundles of surfaces
AU - Yin Li
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30440
UR - https://arxiv.org/abs/2608.30440
AB - We show that for any g≥2, there exist uncountably many non-isomorphic smooth affine threefolds that are Stein deformation equivalent to T^∗Σ_g×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.
ER -