Non-extendable isomorphisms between affine varieties

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 spa...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 172; no. 2; pp. 285 - 291
Main Authors Shpilrain, Vladimir, Yu, Jie-Tai
Format Journal Article
LanguageEnglish
Published Elsevier B.V 24.07.2002
Subjects
Primary 14E09
13B25
secondary 14A10
14E25
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Summary: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.
ISSN:0022-4049
1873-1376
DOI:10.1016/S0022-4049(01)00166-9