On the inverse Galois problem for del Pezzo surfaces of degree 1
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915909511151616 |
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| author | Karras, Luke |
| author_facet | Karras, Luke |
| contents | We solve the inverse Galois problem for del Pezzo surfaces of degree 1 over finite fields completely for 85 of the 112 possible types. We also determine for all 112 types the smallest field of existence. As an aside, we provide an example of a del Pezzo surface of degree 1 in characteristic 2 with more than one generalized Eckardt point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the inverse Galois problem for del Pezzo surfaces of degree 1 Karras, Luke Algebraic Geometry Number Theory 14J26, 14G05, 14G15 We solve the inverse Galois problem for del Pezzo surfaces of degree 1 over finite fields completely for 85 of the 112 possible types. We also determine for all 112 types the smallest field of existence. As an aside, we provide an example of a del Pezzo surface of degree 1 in characteristic 2 with more than one generalized Eckardt point. |
| title | On the inverse Galois problem for del Pezzo surfaces of degree 1 |
| topic | Algebraic Geometry Number Theory 14J26, 14G05, 14G15 |
| url | https://arxiv.org/abs/2604.02036 |