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Fundamentalnaya i Prikladnaya Matematika, 2009, Volume 15, Issue 1, Pages 125–133
(Mi fpm1209)
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Varieties birationally isomorphic to affine $G$-varieties
A. V. Petukhovab a Jacobs University, Bremen, Germany
b M. V. Lomonosov Moscow State University
Abstract:
Let a linear algebraic group $G$ act on an algebraic variety $X$. Classification of all these actions, in particular birational classification, is of great interest. A complete classification related to Galois cohomologies of the group $G$ was established. Another important question is reducibility, in some sense, of this action to an action of $G$ on an affine variety. It has been shown that if the stabilizer of a typical point under the action of a reductive group $G$ on a variety $X$ is reductive, then $X$ is birationally isomorphic to an affine variety $\overline X$ with stable action of $G$. In this paper, I show that if a typical orbit of the action of $G$ is quasiaffine, then the variety $X$ is birationally isomorphic to an affine variety $\overline X$.
Citation:
A. V. Petukhov, “Varieties birationally isomorphic to affine $G$-varieties”, Fundam. Prikl. Mat., 15:1 (2009), 125–133; J. Math. Sci., 166:6 (2010), 773–778
Linking options:
https://www.mathnet.ru/eng/fpm1209 https://www.mathnet.ru/eng/fpm/v15/i1/p125
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Abstract page: | 270 | Full-text PDF : | 119 | References: | 39 | First page: | 2 |
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