Journal of the Ramanujan Mathematical Society

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On the Arithmetic of the Discriminant for Cubic Surfaces


Affiliations
1 Universitat Bayreuth, Mathematisches Institut, Universit¨atsstrasse 30, D-95447 Bayreuth, Germany
2 Universitat Siegen, Departement Mathematik, Walter-Flex-Strasse 3, D-57068 Siegen, Germany
     

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The 27 lines on a smooth cubic surface over Q are acted upon by a finite quotient of Gal(Q/Q). We construct explicit examples such that the operation is via the index two subgroup of the maximal possible group. This is the simple group of order 25 920. Our examples are given in pentahedral normal form with rational coefficients. On the corresponding parameter space, we search for rational points, discuss their asymptotic, and construct an accumulating subvariety.
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  • On the Arithmetic of the Discriminant for Cubic Surfaces

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Authors

Andreas-Stephan Elsenhans
Universitat Bayreuth, Mathematisches Institut, Universit¨atsstrasse 30, D-95447 Bayreuth, Germany
Jorg Jahnel
Universitat Siegen, Departement Mathematik, Walter-Flex-Strasse 3, D-57068 Siegen, Germany

Abstract


The 27 lines on a smooth cubic surface over Q are acted upon by a finite quotient of Gal(Q/Q). We construct explicit examples such that the operation is via the index two subgroup of the maximal possible group. This is the simple group of order 25 920. Our examples are given in pentahedral normal form with rational coefficients. On the corresponding parameter space, we search for rational points, discuss their asymptotic, and construct an accumulating subvariety.