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

Abstract

We construct algebraic families of smooth affine ${\mathbb{A}}^1$-contractible varieties of every dimension $n\ge 4$ 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.

Comments are welcome