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arXiv · 1001.0223

Combinatorial cubic surfaces and reconstruction theorems

Yu. I. Manin
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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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Yu. I. Manin. 2010-01-01. Combinatorial cubic surfaces and reconstruction theorems. https://arxiv.org/abs/1001.0223

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