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4 papers · 1 filter
On cubic surfaces with a rational line
Andreas-Stephan Elsenhans, Jörg Jahnel
We report on our project to construct non-singular cubic surfaces over with a rational line. Our method is to start with degree 4 Del Pezzo surfaces in diagonal form. For th…
On the quasi group of a cubic surface over a finite field
Andreas-Stephan Elsenhans, Jörg Jahnel
We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the…
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…
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…