{"id":"openai-math/An-explicit-failure-of-complex-affine-space-cancellation","pdf":"https://github.com/openai/math/blob/main/preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-explicit-failure-of-complex-affine-space-cancellation-September-23-2026","tags":["algebraic-geometry","affine-space-cancellation"],"score":0,"title":"An explicit failure of complex affine-space cancellation","domain":"Algebraic and complex geometry","family":"047","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We construct an explicit integral complex affine fourfold X with $`X\\times\\mathbb A^1\\cong\\mathbb A^5`$ but $`X\\not\\cong\\mathbb A^4`$. This gives a negative answer to Zariski's affine-space cancellation problem over ℂ in dimension four. The same construction disproves the Stable Coordinate Conjecture in ambient dimension five and yields smooth 𝔸 3 -fibrations over 𝔸 1 and 𝔸 2 that are not Zariski-locally trivial. These fibrations disprove the Dolgachev–Weisfeiler affine-fibration conjecture over these bases.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Zariski cancellation and affine fibrations over the complex numbers"}