A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces
Algebraic Geometry
2007-05-23 v2
Abstract
It is well-known that a Severi-Brauer surface has a rational point if and only if it is isomorphic to the projective plane. Given a Severi-Brauer surface, we study the problem to decide whether such an isomorphism to the projective plane, or such a rational point, does exist; and to construct such an isomorphism or such a point in the affirmative case. We give an algorithm using Lie algebra techniques. The algorithm has been implemented in Magma.
Cite
@article{arxiv.math/0501157,
title = {A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces},
author = {Willem A. de Graaf and Michael Harrison and Jana Pilnikova and Josef Schicho},
journal= {arXiv preprint arXiv:math/0501157},
year = {2007}
}
Comments
16 pages some minor revisions