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Abstract

We study the following cancellation problem over an algebraically closed field $\mathbb K$ of characteristic zero. Let $X$, $Y$ be affine varieties such that $X\times\mathbb K^m\cong Y\times\mathbb K^m$ for some $m$. Assume that $X$ is non-uniruled at infinity. Does it follow that $X\cong Y$? We prove a result implying the affirmative answer in case $X$ is either unirational or an algebraic line bundle. However, the general answer is negative and we give as a counterexample some affine surfaces.