On algorithmic unsolvability of the problem embeddability of algebraic varieties over a field of characteristic zero
Algebraic Geometry
2019-07-01 v5 Logic
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.
Keywords
Cite
@article{arxiv.1812.01883,
title = {On algorithmic unsolvability of the problem embeddability of algebraic varieties over a field of characteristic zero},
author = {A. J. Kanel-Belov and A. A. Chilikov},
journal= {arXiv preprint arXiv:1812.01883},
year = {2019}
}
Comments
17 pages, in Russian