2010/06/03 by Andreas-Stephan Elsenhans, Elsenhans, Andreas-Stephan, Jörg Jahnel +1
Mathematics · #11G50 #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 11G35 #Secondary 14J20 #math.AG #math.NT #msc:11G35 #msc:11G50 #msc:14J20 #msc:14J45
paper · pdf · doi:10.48550/arxiv.1006.0721
arxiv created 2010/06/03 · arxiv updated 2010/07/27
We construct explicit examples of cubic surfaces over \bbQ such that the 27 lines are acted upon by the index two subgroup of the maximal possible Galois group. This is the simple group of order 25 920. Our examples are given in pentahedral normal form with rational coefficients. For such cubic surfaces, we study the discriminant and show its relation to the index two subgroup. On the corresponding parameter space, we search for rational points, discuss their asymptotic, and construct an accumulating subvariety.