# A note on the stable equivalence problem

Poloni, Pierre-Marie. (2015) A note on the stable equivalence problem. Journal of the Mathematical Society of Japan, Vol. 67 , H. 2. pp. 753-761.

Full text not available from this repository.

Official URL: http://edoc.unibas.ch/dok/A6263176

We provide counterexamples to the stable equivalence problem in every dimension $dgeq2$. That means that we construct hypersurfaces $H_1, H_2subsetC^{d+1}$ whose cylinders $H_1timesC$ and $H_2timesC$ are equivalent hypersurfaces in $C^{d+2}$, although $H_1$ and $H_2$ themselves are not equivalent by an automorphism of $C^{d+1}$. We also give, for every $dgeq2$, examples of two non-isomorphic algebraic varieties of dimension $d$ which are biholomorphic.