Journal of the Mathematical Society of Japan

A note on the stable equivalence problem

Pierre-Marie POLONI

Full-text: Open access

Abstract

We provide counterexamples to the stable equivalence problem in every dimension $d\geq2$. That means that we construct hypersurfaces $H_1, H_2\subset\C^{d+1}$ 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.

Article information

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

Dates
First available in Project Euclid: 21 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1429624602

Digital Object Identifier
doi:10.2969/jmsj/06720753

Mathematical Reviews number (MathSciNet)
MR3340194

Zentralblatt MATH identifier
1338.14058

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

Keywords
equivalence of hypersurfaces stable equivalence locally nilpotent derivations exotic models

Citation

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. https://projecteuclid.org/euclid.jmsj/1429624602


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