Geometry and topology · Oct 6, 2026

Zariski cancellation and affine fibrations over the complex numbers

Constructs an integral complex affine fourfold

X\not\cong\mathbb A^4

with

X\times\mathbb A^1\cong\mathbb A^5

, disproving affine-space cancellation over ℂ in dimension four. It also disproves the Dolgachev–Weisfeiler affine-fibration conjecture: smooth surjections

X\to\mathbb A^1

and

\mathbb A^5\to\mathbb A^2

have every residue-field fiber isomorphic to affine three-space but are not Zariski-locally trivial.

Contributors

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Sources

openai/math catalogue entry ↗
Formalization scope note ↗