A determinant on birational maps of Severi-Brauer surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917913659703296 |
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| author | Kurz, Elias |
| author_facet | Kurz, Elias |
| contents | We define a determinant on the group of automorphisms of non-trivial Severi-Brauer surfaces over a perfect field. Using the generators and relations, we extend this determinant to birational maps between Severi-Brauer surfaces. Using this determinant and a group homomorphism found in arXiv:2211.17123 we can determine the abelianization of the group of birational transformations of a non-trivial Severi-Brauer surface. This is the first example of an abelianization of the group of birational transformations of a geometrically rational surface where the automorphisms are non trivial. Using the abelianization we find maximal subgroups of the group of birational transformations of a non-trivial Severi-Brauer surface over a perfect field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A determinant on birational maps of Severi-Brauer surfaces Kurz, Elias Algebraic Geometry 14E07, 14E05, 14E30, 14J45, 20F05, 20L05 We define a determinant on the group of automorphisms of non-trivial Severi-Brauer surfaces over a perfect field. Using the generators and relations, we extend this determinant to birational maps between Severi-Brauer surfaces. Using this determinant and a group homomorphism found in arXiv:2211.17123 we can determine the abelianization of the group of birational transformations of a non-trivial Severi-Brauer surface. This is the first example of an abelianization of the group of birational transformations of a geometrically rational surface where the automorphisms are non trivial. Using the abelianization we find maximal subgroups of the group of birational transformations of a non-trivial Severi-Brauer surface over a perfect field. |
| title | A determinant on birational maps of Severi-Brauer surfaces |
| topic | Algebraic Geometry 14E07, 14E05, 14E30, 14J45, 20F05, 20L05 |
| url | https://arxiv.org/abs/2502.02981 |