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Rationality of homogeneous varieties


Authors: CheeWhye Chin and De-Qi Zhang
Journal: Trans. Amer. Math. Soc. 369 (2017), 2651-2673
MSC (2010): Primary 14E08, 14M17, 14M20
DOI: https://doi.org/10.1090/tran/6728
Published electronically: April 15, 2016
MathSciNet review: 3592523
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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) \leqslant 10$ and $ \operatorname {char}(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 $ \operatorname {char}(k) \neq 2$), or type $ B_3$ or $ G_2$ (when $ \operatorname {char}(k) = 0$).


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Additional Information

CheeWhye Chin
Affiliation: Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
Email: cheewhye@nus.edu.sg

De-Qi Zhang
Affiliation: Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
Email: matzdq@nus.edu.sg

DOI: https://doi.org/10.1090/tran/6728
Keywords: Homogeneous variety, rationality
Received by editor(s): March 9, 2015
Received by editor(s) in revised form: April 15, 2015
Published electronically: April 15, 2016
Article copyright: © Copyright 2016 American Mathematical Society