Rationality of homogeneous varieties
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- by CheeWhye Chin and De-Qi Zhang PDF
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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 $\operatorname {char}(k) = 0$).References
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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
- MR Author ID: 187025
- ORCID: 0000-0003-0139-645X
- Email: matzdq@nus.edu.sg
- Received by editor(s): March 9, 2015
- Received by editor(s) in revised form: April 15, 2015
- Published electronically: April 15, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2651-2673
- MSC (2010): Primary 14E08, 14M17, 14M20
- DOI: https://doi.org/10.1090/tran/6728
- MathSciNet review: 3592523