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arXiv · 2604.01497

Galois group of exceptional curves on the generic del Pezzo surface

Xinyu Fang
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Abstract

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.

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Xinyu Fang. 2026-04-02. Galois group of exceptional curves on the generic del Pezzo surface. https://arxiv.org/abs/2604.01497

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