Galois group of exceptional curves on the generic del Pezzo surface
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912997677465600 |
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| author | Fang, Xinyu |
| author_facet | Fang, Xinyu |
| contents | We prove that the Galois action on the exceptional curves on the generic del Pezzo surface of degree $d$ is maximal for all degrees $d$ and over any field $k$. As a consequence of the case $d=3$, we deduce that over $\mathbb{F}_q(u)$, 100% of cubic surfaces have no Brauer-Manin obstruction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01497 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Galois group of exceptional curves on the generic del Pezzo surface Fang, Xinyu Algebraic Geometry Number Theory 14J26 (Primary) 14J10, 14G12, 11G35 (Secondary) We prove that the Galois action on the exceptional curves on the generic del Pezzo surface of degree $d$ is maximal for all degrees $d$ and over any field $k$. As a consequence of the case $d=3$, we deduce that over $\mathbb{F}_q(u)$, 100% of cubic surfaces have no Brauer-Manin obstruction. |
| title | Galois group of exceptional curves on the generic del Pezzo surface |
| topic | Algebraic Geometry Number Theory 14J26 (Primary) 14J10, 14G12, 11G35 (Secondary) |
| url | https://arxiv.org/abs/2604.01497 |