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Mathematics > Algebraic Geometry

arXiv:1812.01883 (math)
[Submitted on 5 Dec 2018 (v1), last revised 28 Jun 2019 (this version, v5)]

Title:On algorithmic unsolvability of the problem embeddability of algebraic varieties over a field of characteristic zero

Authors:A.J.Kanel-Belov, A.A.Chilikov
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Abstract: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.
Comments: 17 pages, in Russian
Subjects: Algebraic Geometry (math.AG); Logic (math.LO)
MSC classes: 14R10, 03D35
Cite as: arXiv:1812.01883 [math.AG]
  (or arXiv:1812.01883v5 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.01883

Submission history

From: Alexei Kanel-Belov Prof. [view email]
[v1] Wed, 5 Dec 2018 09:58:41 UTC (9 KB)
[v2] Mon, 7 Jan 2019 10:27:41 UTC (12 KB)
[v3] Mon, 21 Jan 2019 23:44:41 UTC (15 KB)
[v4] Wed, 5 Jun 2019 04:53:06 UTC (12 KB)
[v5] Fri, 28 Jun 2019 09:43:35 UTC (15 KB)
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