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Algebraic families of higher dimensional $\mathbb{A}^{1}$-contractible affine varieties non-isomorphic to affine spaces (2501.09613v1)

Published 16 Jan 2025 in math.AG and math.AC

Abstract: We construct algebraic families of smooth affine $\mathbb{A}1$-contractible varieties of every dimension $n\geq 4$ over fields of characteristic zero which are non-isomorphic to affine spaces and potential counterexamples to the Zariski Cancellation Problem. We further prove that these families of varieties are also counter examples to the generalized Cancellation problem.

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