A characteristic-zero counterexample to Lipman–Zariski

Constructs a singular normal affine complex surface with free rank-two tangent sheaf, disproving the characteristic-zero Lipman–Zariski conjecture.

Manuscript

A singular normal affine surface with free tangent sheaf

September 23, 2026 · source · cite as \cite{OAI:A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026}

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.

Result 048 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.