Automorphisms of quartic surfaces and Cremona transformations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913322361683968 |
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| author | Paiva, Daniela Quedo, Ana |
| author_facet | Paiva, Daniela Quedo, Ana |
| contents | In this paper, we consider the problem of determining which automorphisms of a smooth quartic surface $S \subset \mathbb{P}^3$ are induced by a Cremona transformation of $\mathbb{P}^3$. We provide the first steps towards a complete solution of this problem when $ρ(S)=2$. In particular, we give several examples of quartics whose automorphism groups are generated by involutions, but no non-trivial automorphism is induced by a Cremona transformation of $\mathbb{P}^3$, giving a negative answer for Oguiso's question of whether every automorphism of finite order of a smooth quartic surface $S\subset \mathbb{P}^3$ is induced by a Cremona transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09014 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Automorphisms of quartic surfaces and Cremona transformations Paiva, Daniela Quedo, Ana Algebraic Geometry In this paper, we consider the problem of determining which automorphisms of a smooth quartic surface $S \subset \mathbb{P}^3$ are induced by a Cremona transformation of $\mathbb{P}^3$. We provide the first steps towards a complete solution of this problem when $ρ(S)=2$. In particular, we give several examples of quartics whose automorphism groups are generated by involutions, but no non-trivial automorphism is induced by a Cremona transformation of $\mathbb{P}^3$, giving a negative answer for Oguiso's question of whether every automorphism of finite order of a smooth quartic surface $S\subset \mathbb{P}^3$ is induced by a Cremona transformation. |
| title | Automorphisms of quartic surfaces and Cremona transformations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2302.09014 |