The most symmetric smooth cubic surface over a finite field of characteristic $2$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916323821355008 |
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| author | Vikulova, Anastasia V. |
| author_facet | Vikulova, Anastasia V. |
| contents | In this paper we find the largest automorphism group of a smooth cubic surface over any finite field of characteristic $2.$ We prove that if the order of the field is a power of $4,$ then the automorphism group of maximal order of~a~smooth cubic surface over this field is $\mathrm{PSU}_4(\mathbb{F}_2).$ If the order of the field of characteristic $2$ is not a power of $4,$ then we prove that the automorphism group of maximal order of a smooth cubic surface over this field is the symmetric group of degree $6.$ Moreover, we prove that smooth cubic surfaces with such properties are unique up to isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17032 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The most symmetric smooth cubic surface over a finite field of characteristic $2$ Vikulova, Anastasia V. Algebraic Geometry 14J50 In this paper we find the largest automorphism group of a smooth cubic surface over any finite field of characteristic $2.$ We prove that if the order of the field is a power of $4,$ then the automorphism group of maximal order of~a~smooth cubic surface over this field is $\mathrm{PSU}_4(\mathbb{F}_2).$ If the order of the field of characteristic $2$ is not a power of $4,$ then we prove that the automorphism group of maximal order of a smooth cubic surface over this field is the symmetric group of degree $6.$ Moreover, we prove that smooth cubic surfaces with such properties are unique up to isomorphism. |
| title | The most symmetric smooth cubic surface over a finite field of characteristic $2$ |
| topic | Algebraic Geometry 14J50 |
| url | https://arxiv.org/abs/2312.17032 |