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Contemporary Mathematics, 2012, Volume 566, Pages 99–118
DOI: https://doi.org/10.1090/conm/566/11217
(Mi conm3)
 

This article is cited in 2 scientific papers (total in 2 papers)

Combinatorial cubic surfaces and reconstruction theorems

Yu. I. Manin

Max Planck Institute for Mathematics
Citations (2)
Abstract: This note contains a solution to the following problem: reconstruct the definition field and the equation of a projective cubic surface, using only combinatorial information about the set of its rational points. This information is encoded in two relations: collinearity and coplanarity of certain subsets of points. We solve this problem, assuming mild "general position" properties. This study is motivated by an attempt to address the Mordell-Weil problem for cubic surfaces using essentially model theoretic methods. However, the language of model theory is not used explicitly.
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Document Type: Article
Language: English
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