Non-extendable isomorphisms between affine varieties

Vladimir Shpilrain; Jie-Tai Yu

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arXiv · math/0110232

Non-extendable isomorphisms between affine varieties

Vladimir Shpilrain·Jie-Tai Yu

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Abstract

In this paper, we report several large classes of affine varieties (over an arbitrary field $K$ of characteristic 0) with the following property: each variety in these classes has an isomorphic copy such that the corresponding isomorphism cannot be extended to an automorphism of the ambient affine space $K^n$. This implies, in particular, that each of these varieties has at least two inequivalent embeddings in $K^n$. The following application of our results seems interesting: we show that lines in $K^2$ are distinguished among irreducible algebraic retracts by the property of having a unique embedding in $K^2$.

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BibTeX RIS

Vladimir Shpilrain, Jie-Tai Yu. 2001-10-21. Non-extendable isomorphisms between affine varieties. https://arxiv.org/abs/math/0110232

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