Construction algorithms for rational cubic surfaces. (March 2017) - González-Sánchez, Jon; Polo-Blanco, Irene
Abstract: By a criterion of Swinnerton-Dyer it is known that a smooth cubic surface S defined over Q is birationally trivial over Q if and only if S ( Q ) ≠ ∅ and S contains a Gal ( Q ‾, Q ) -stable set of 2, 3 or 6 skew lines. In this text we describe birationally trivial smooth cubic surfaces over Q and provide algorithms to construct explicit cubic surfaces for each of the cases in Swinnerton-Dyer's criterion.