Rational surfaces and canonical dimension of PGL_6
Algebraic Geometry
2007-05-23 v1
Abstract
The "canonical dimension" of an algebraic group over a field by definition is the maximum of the canonical dimensions of principal homogenous spaces under that group. Over a field of characteristic zero, we prove that the canonical dimension of the projective linear group PGL_6 is 3. We give two distinct proofs, both of which rely on the birational classification of rational surfaces over a nonclosed field. One of the proofs involves taking a novel look at del Pezzo surfaces of degree 6.
Cite
@article{arxiv.math/0611777,
title = {Rational surfaces and canonical dimension of PGL_6},
author = {Jean-Louis Colliot-Thélène and Nikita A. Karpenko and Alexander S. Merkurjev},
journal= {arXiv preprint arXiv:math/0611777},
year = {2007}
}