Archiv der Mathematik

, Volume 98, Issue 3, pp 229–234 | Cite as

On cubic surfaces with a rational line



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.

Mathematics Subject Classification (2010)

Primary 14J26 Secondary 14G25 11G35 


Cubic surface Degree 4 Del Pezzo surface Explicit Galois descent 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BayreuthBayreuthGermany
  2. 2.Département MathematikUniversität SiegenSiegenGermany

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