Journal of the Mathematical Society of Japan

A note on the stable equivalence problem

Pierre-Marie POLONI

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We provide counterexamples to the stable equivalence problem in every dimension $d\geq2$. That means that we construct hypersurfaces $H_1, H_2\subset\C^{d+1}$ whose cylinders $H_1\times\C$ and $H_2\times\C$ 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 $d\geq2$, examples of two non-isomorphic algebraic varieties of dimension $d$ which are biholomorphic.

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J. Math. Soc. Japan, Volume 67, Number 2 (2015), 753-761.

First available in Project Euclid: 21 April 2015

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Zentralblatt MATH identifier

Primary: 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]

equivalence of hypersurfaces stable equivalence locally nilpotent derivations exotic models


POLONI, Pierre-Marie. A note on the stable equivalence problem. J. Math. Soc. Japan 67 (2015), no. 2, 753--761. doi:10.2969/jmsj/06720753.

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