Abstract
We report on our project to construct non-singular cubic surfaces over \({\mathbb{Q}}\) with a rational line. Our method is to start with degree 4 Del Pezzo surfaces in diagonal form. For these, we develop an explicit version of Galois descent.
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The first author was supported in part by the Deutsche Forschungsgemeinschaft (DFG) through a funded research project.
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Elsenhans, AS., Jahnel, J. On cubic surfaces with a rational line. Arch. Math. 98, 229–234 (2012). https://doi.org/10.1007/s00013-012-0356-4
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DOI: https://doi.org/10.1007/s00013-012-0356-4