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arXiv · 2311.07317

Singular del Pezzo surfaces over finite fields

H. Uppal
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Abstract

If $X$ is a singular del Pezzo surface of degree $d$ over a finite field $\mathbb{F}_{q}$ with only rational double point singularities, does there always exist a smooth $\mathbb{F}_{q}$-point on $X$? We show that this is true for $d\geq 3$ and give counterexamples in the case of $d=2$.

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H. Uppal. 2023-11-13. Singular del Pezzo surfaces over finite fields. https://arxiv.org/abs/2311.07317

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