Affine homogeneous varieties and suspensions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911810132639744 |
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| author | Arzhantsev, Ivan Zaitseva, Yulia |
| author_facet | Arzhantsev, Ivan Zaitseva, Yulia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06170 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Affine homogeneous varieties and suspensions Arzhantsev, Ivan Zaitseva, Yulia Algebraic Geometry 14M17, 14R20 (Primary) 14J50, 14L30 (Secondary) 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. |
| title | Affine homogeneous varieties and suspensions |
| topic | Algebraic Geometry 14M17, 14R20 (Primary) 14J50, 14L30 (Secondary) |
| url | https://arxiv.org/abs/2309.06170 |