Open Access
April, 2015 A note on the stable equivalence problem
Pierre-Marie POLONI
J. Math. Soc. Japan 67(2): 753-761 (April, 2015). DOI: 10.2969/jmsj/06720753


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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Pierre-Marie POLONI. "A note on the stable equivalence problem." J. Math. Soc. Japan 67 (2) 753 - 761, April, 2015.


Published: April, 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1338.14058
MathSciNet: MR3340194
Digital Object Identifier: 10.2969/jmsj/06720753

Primary: 14L30 , 14R10

Keywords: equivalence of hypersurfaces , exotic models , locally nilpotent derivations , stable equivalence

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 2 • April, 2015
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