26 citations · 102 across the 28 of their papers we have counts for
9 papers · 1 filter
On the Brauer-Manin obstruction for cubic surfaces
Andreas-Stephan Elsenhans, Jörg Jahnel
We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over such that $\Br(S)/\Br(\bbQ)$ is of order two or four. This covers the vast majori…
Determinantal quartics and the computation of the Picard group
Andreas-Stephan Elsenhans, Jörg Jahnel
We test the methods for computing the Picard group of a surface in a situation of high rank. The examples chosen are resolutions of quartics in $\bP^3$ having 14 singularities…
Rational points on diagonal quartic surfaces
Elsenhans, Andreas-Stephan
We searched up to height for rational points on diagonal quartic surfaces. The computations fill several gaps in earlier lists computed by Pinch, Swinnerton-Dyer, and Bright…
The Picard group of a surface and its reduction modulo
Andreas-Stephan Elsenhans, Jörg Jahnel
We present a method to compute the geometric Picard rank of a surface over . Contrary to a widely held belief, we show it is possible to verify Picard rank using red…
On the computation of the Picard group for surfaces
Andreas-Stephan Elsenhans, Jörg Jahnel
We construct examples of surfaces of geometric Picard rank . Our method is a refinement of that of R. van Luijk. It is based on an analysis of the Galois module structure o…
Cubic surfaces with a Galois invariant pair of Steiner trihedra
Andreas-Stephan Elsenhans, Jörg Jahnel
We present a method to construct non-singular cubic surfaces over with a Galois invariant pair of Steiner trihedra. We start with cubic surfaces in a form generalizing that…