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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