A singular normal affine surface with free tangent sheaf
We construct a singular normal affine complex surface whose tangent sheaf is free of rank two. This disproves the Lipman–Zariski conjecture in characteristic zero.
Cite
@misc{OAI:A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026,
author = {{OpenAI}},
title = {{A singular normal affine surface with free tangent sheaf}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026/paper.pdf}{OAI:A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026}},
year = {2026}
}