{"id":"openai-math/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre","pdf":"https://github.com/openai/math/blob/main/preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-explicit-noncoordinate-polynomial-with-affine-three-space-zero-fibre-September-24-2026","tags":["algebraic-geometry","abhyankar-sathaye-conjecture"],"score":0,"title":"An explicit noncoordinate polynomial with affine three-space zero fibre","domain":"Algebraic and complex geometry","family":"049","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We construct an explicit counterexample to the Abhyankar–Sathaye conjecture: a noncoordinate polynomial in four complex variables whose zero fibre is affine three-space. Adjoining variables gives counterexamples in every ambient dimension at least four.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"A stable-coordinate counterexample in four variables"}