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arXiv · 1504.05402

Rationality of homogeneous varieties

CheeWhye Chin·De-Qi Zhang
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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).

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CheeWhye Chin, De-Qi Zhang. 2015-04-21. Rationality of homogeneous varieties. https://arxiv.org/abs/1504.05402

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