Construction algorithms for rational cubic surfaces. (March 2017)

• Record Type: Journal Article
• Authors: González-Sánchez, Jon; Polo-Blanco, Irene
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 2
• Page Start: 309
• Page End: 326
• Publication Date: 2017-03
• Subjects: Del Pezzo -- Rational surface -- Cubic surface -- Parametrization -- Algorithm; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.02.010
• Languages: English
• ISSNs: 0747-7171

Abstract

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.