A note on the stable equivalence problem

Pierre-Marie Poloni (1)

1 Unibas - Université de Bâle = University of Basel = Basel Universität

We provide counterexamples to the stable equivalence problem in every dimension $d\geq2$. That means that we construct hypersurfaces $H_1, H_2\subset\mathbb{C}^{d+1}$ whose cylinders $H_1\times\mathbb{C}$ and $H_2\times\mathbb{C}$ are equivalent hypersurfaces in $\mathbb{C}^{d+2}$, although $H_1$ and $H_2$ themselves are not equivalent by an automorphism of $\mathbb{C}^{d+1}$. We also give, for every $d\geq2$, examples of two non-isomorphic algebraic varieties of dimension $d$ which are biholomorphic.

Domaines: Géométrie algébrique [math.AG]

Pierre-Marie Poloni. A note on the stable equivalence problem. 2013. ⟨hal-00851110⟩