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arXiv · 2202.11030

Birational classification of pointless del Pezzo surfaces of degree 8

Andrey Trepalin
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Abstract

Let k be a perfect field. Recently J.-L. Colliot-Th\'el\`ene showed that two pointless quadric surfaces over k are birationally equivalent if and only if they are isomorphic. We show that this result holds for arbitrary del Pezzo surfaces of degree $8$ with the Picard number $1$, and describe minimal surfaces birationally equivalent to a given pointless del Pezzo surface of degree $8$.

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Andrey Trepalin. 2022-02-22. Birational classification of pointless del Pezzo surfaces of degree 8. https://arxiv.org/abs/2202.11030

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