Generators for Cubic Surfaces with two Skew Lines over Finite Fields
Number Theory
2013-12-23 v2
Abstract
Let S be a smooth cubic surface defined over a field K. As observed by Segre and Manin, there is a secant and tangent process on S that generates new K-rational points from old. It is natural to ask for the size of a minimal generating set for S(K). In a recent paper, for fields K with at least 13 elements, Siksek showed that if S contains a skew pair of K-lines then S(K) can be generated from one point. In this paper we prove the corresponding version of this result for fields K having at least 4 elements, and slightly milder results for #K=2 or 3.
Cite
@article{arxiv.1205.6392,
title = {Generators for Cubic Surfaces with two Skew Lines over Finite Fields},
author = {Jenny Cooley},
journal= {arXiv preprint arXiv:1205.6392},
year = {2013}
}
Comments
10 pages. arXiv admin note: text overlap with arXiv:1012.1838 by other authors