{"id":"openai-math/A-singular-normal-affine-surface-with-free-tangent-sheaf","pdf":"https://github.com/openai/math/blob/main/preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-singular-normal-affine-surface-with-free-tangent-sheaf-September-23-2026","tags":["algebraic-geometry","affine-surfaces","tangent-sheaf"],"score":0,"title":"A singular normal affine surface with free tangent sheaf","domain":"Algebraic and complex geometry","family":"048","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"A characteristic-zero counterexample to Lipman–Zariski"}