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Article Dans Une Revue Bulletin of the London Mathematical Society Année : 2016

Affine-ruled varieties without the Laurent cancellation property

Résumé

We describe a method to construct hypersurfaces of the complex affine $n$-space with isomorphic $\mathbb{C}^*$-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, that is, hypersurfaces that are non isomorphic, although their $\mathbb{C}^*$-cylinders are isomorphic as abstract algebraic varieties. We also provide examples of non isomorphic varieties $X$ and $Y$ with isomorphic cartesian squares $X\times X$ and $Y\times Y$.
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Dates et versions

hal-01205277 , version 1 (25-09-2015)

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Adrien Dubouloz, Pierre-Marie Poloni. Affine-ruled varieties without the Laurent cancellation property. Bulletin of the London Mathematical Society, 2016, 48 (5), pp.822-834. ⟨10.1112/blms/bdw045⟩. ⟨hal-01205277⟩
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