A note on the stable equivalence problem
Year: 2013
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Poloni, Pierre-Marie
Institution: University of Basel
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4290441980