An explicit failure of complex affine-space cancellation
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.
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