Rationality of homogeneous varieties
Algebraic Geometry
2018-09-24 v2
Abstract
Let G be a connected linear algebraic group over an algebraically closed field k, and let H be a connected closed subgroup of G. We prove that the homogeneous variety G/H is a rational variety over k whenever H is solvable, or when dim(G/H) < 11 and characteristic(k) = 0. When H is of maximal rank in G, we also prove that G/H is rational if the maximal semisimple quotient of G is isogenous to a product of almost-simple groups of type A, type C (when characteristic(k) is not 2), or type B_3 or G_2 (when characteristic(k) = 0).
Keywords
Cite
@article{arxiv.1504.05402,
title = {Rationality of homogeneous varieties},
author = {CheeWhye Chin and De-Qi Zhang},
journal= {arXiv preprint arXiv:1504.05402},
year = {2018}
}
Comments
Transactions of the American Mathematical Society (to appear); Lemma 2.2 statement and Lemma 2.6 final part are slightly edited