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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Rationality of homogeneous varieties
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by CheeWhye Chin and De-Qi Zhang PDF
Trans. Amer. Math. Soc. 369 (2017), 2651-2673 Request permission

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