Andreas-Stephan Elsenhans, Jörg Jahnel
Published 2011-06-21Version 1
We report on our project to construct non-singular cubic surfaces over $\bbQ$ 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.
Del Pezzo surfaces of degree four violating the Hasse principle are Zariski dense in the moduli scheme
Cubic surfaces with a Galois invariant pair of Steiner trihedra
Del Pezzo surfaces of degree 1 and jacobians
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