Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 047-01. An explicit failure of complex affine-space cancellation
Manuscript map · lines 3475–3484
OpenAI@2026-10-07#rem:oai-p-047-01
Authors: OpenAI. Family 047.
Title: An explicit failure of complex affine-space cancellation.
Abstract: 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 𝔸3-fibrations over 𝔸1 and 𝔸2 that are not Zariski-locally trivial. These fibrations disprove the Dolgachev–Weisfeiler affine-fibration conjecture over these bases.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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