Affine homogeneous varieties and suspensions
| Autor: | Arzhantsev, Ivan, Zaitseva, Yulia |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Research in the Mathematical Sciences 11 (2024), no. 2, article 27 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40687-024-00438-x |
| Popis: | An algebraic variety $X$ is called a homogeneous variety if the automorphism group $\mathrm{Aut}(X)$ 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. Comment: 12 pages |
| Databáze: | arXiv |
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