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Affine homogeneous varieties and suspensions

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Abstract

An algebraic variety X is called a homogeneous variety if the automorphism group \({{\,\textrm{Aut}\,}}(X)\) acts on X transitively, and a homogeneous space if there exists a transitive action of an algebraic group on X. We prove a criterion of smoothness of a suspension to construct a wide class of homogeneous varieties. As an application, we give criteria for a Danielewski surface to be a homogeneous variety and a homogeneous space. Also, we construct affine suspensions of arbitrary dimension that are homogeneous varieties but not homogeneous spaces.

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  1. Faculty of Computer Science, HSE University, Pokrovsky Boulvard 11, Moscow, Russia, 109028

    Ivan Arzhantsev & Yulia Zaitseva

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  1. Ivan Arzhantsev
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  2. Yulia Zaitseva
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Correspondence to Yulia Zaitseva.

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This research was supported by the Ministry of Science and Higher Education of the Russian Federation, Agreement 075-15-2022-289 date 06/04/2022.

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Arzhantsev, I., Zaitseva, Y. Affine homogeneous varieties and suspensions. Res Math Sci 11, 27 (2024). https://doi.org/10.1007/s40687-024-00438-x

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