Algebraic and complex geometry·OpenAI Math·Result 048
A characteristic-zero counterexample to Lipman–Zariski
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
A singular normal affine surface with free tangent sheaf
The animation for this result has not been released yet. Subscribe on YouTube to catch it.
What OpenAI claims
Constructs a singular normal affine complex surface with free rank-two tangent sheaf, disproving the characteristic-zero Lipman–Zariski conjecture.
Paper
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.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Related results in Algebraic and complex geometry
- 049A stable-coordinate counterexample in four variablesLean
- 050A counterexample to Griffiths’ positivity conjectureLean
- 051Kobayashi’s canonical-ampleness conjecture
- 052Tangent splittings and product decompositionsLean
- 053A counterexample to Pixton completeness in Chow
- 054Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations
