Combinatorial cubic surfaces and reconstruction theorems
Yu. I. Manin · Contemporary mathematics - American Mathematical Society · 2012
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.