Generators of the plane Cremona group over the field with two elements
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2020
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910321456709632 |
|---|---|
| author | Schneider, Julia |
| author_facet | Schneider, Julia |
| contents | The plane Cremona group over the finite field $\mathbb{F}_2$ is generated by three infinite families and finitely many birational maps with small base orbits. One family preserves the pencil of lines through a point, the other two preserve the pencil of conics through four points that form either one Galois orbit of size 4, or two Galois orbits of size 2. For each family, we give a generating set that is parametrized by the rational functions over $\mathbb{F}_2$. Moreover, we describe the finitely many remaining maps and give an upper bound on the number needed to generate the Cremona group. Finally, we prove that the plane Cremona group over $\mathbb{F}_2$ is generated by involutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_07991 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Generators of the plane Cremona group over the field with two elements Schneider, Julia Algebraic Geometry 14E07 14G15 14E05 11G25 14J26 The plane Cremona group over the finite field $\mathbb{F}_2$ is generated by three infinite families and finitely many birational maps with small base orbits. One family preserves the pencil of lines through a point, the other two preserve the pencil of conics through four points that form either one Galois orbit of size 4, or two Galois orbits of size 2. For each family, we give a generating set that is parametrized by the rational functions over $\mathbb{F}_2$. Moreover, we describe the finitely many remaining maps and give an upper bound on the number needed to generate the Cremona group. Finally, we prove that the plane Cremona group over $\mathbb{F}_2$ is generated by involutions. |
| title | Generators of the plane Cremona group over the field with two elements |
| topic | Algebraic Geometry 14E07 14G15 14E05 11G25 14J26 |
| url | https://arxiv.org/abs/2008.07991 |