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Preprint Number 1530

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1530. A.J.Kanel-Belov, A.A.Chilikov
On algorithmic unsolvability of the problem embeddability of algebraic varieties over a field of characteristic zero

Submission date: 5 December 2018


(In Russian)
We show that for two afii varieties over an arbitrary field of characteristic zero, there is no general form of an algorithm for checking the presence of an embedding of one algebraic variety in another. Moreover, we establish this for affine varieties whose coordinate rings are given by generators and defining relations. Moreover, one of these varieties can be taken as an affine space, and in the case of a field of real numbers, an affine line.

Mathematics Subject Classification: 1812.01883

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Full text arXiv 1812.01883: pdf, ps.

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