Galois points and Cremona transformations
Glasgow mathematical journal, Tome 66 (2024) no. 3, pp. 471-478
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In this article, we study Galois points of plane curves and the extension of the corresponding Galois group to $\mathrm{Bir}(\mathbb{P}^2)$. We prove that if the Galois group has order at most $3$, it always extends to a subgroup of the Jonquières group associated with the point $P$. Conversely, with a degree of 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 $P$. In addition, we also give an example of a Galois extension whose Galois group cannot be extended to Cremona transformations.
Mots-clés :
Galois points, Cremona transformations, Galois groups, Jonquières maps
Abouelsaad, Ahmed. Galois points and Cremona transformations. Glasgow mathematical journal, Tome 66 (2024) no. 3, pp. 471-478. doi: 10.1017/S0017089524000090
@article{10_1017_S0017089524000090,
author = {Abouelsaad, Ahmed},
title = {Galois points and {Cremona} transformations},
journal = {Glasgow mathematical journal},
pages = {471--478},
year = {2024},
volume = {66},
number = {3},
doi = {10.1017/S0017089524000090},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089524000090/}
}
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