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 $Y\times Y$.
Origine | Fichiers produits par l'(les) auteur(s) |
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