Galois Points and Cremona Transformations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912133259722752 |
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| author | Abouelsaad, Ahmed |
| author_facet | Abouelsaad, Ahmed |
| contents | In this article, we study Galois points of plane curves and the extension of the corresponding Galois group to $\mathrm{Bir}(\mathbb{P}^2)$. If the Galois group has order at most $3$, we prove that it always extends to a subgroup of the Jonquières group associated to the point $P$. In degree at least $4$, we prove that it is false. We provide an example of a Galois extension whose Galois group is extendable to Cremona transformations but not to a group of de Jonquières maps with respect to $P$. We also give an example of a Galois extension whose Galois group cannot be extended to Cremona transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00324 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Galois Points and Cremona Transformations Abouelsaad, Ahmed Algebraic Geometry Number Theory 14E07, 14H05, 14H50 In this article, we study Galois points of plane curves and the extension of the corresponding Galois group to $\mathrm{Bir}(\mathbb{P}^2)$. If the Galois group has order at most $3$, we prove that it always extends to a subgroup of the Jonquières group associated to the point $P$. In degree at least $4$, we prove that it is false. We provide an example of a Galois extension whose Galois group is extendable to Cremona transformations but not to a group of de Jonquières maps with respect to $P$. We also give an example of a Galois extension whose Galois group cannot be extended to Cremona transformations. |
| title | Galois Points and Cremona Transformations |
| topic | Algebraic Geometry Number Theory 14E07, 14H05, 14H50 |
| url | https://arxiv.org/abs/2302.00324 |