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arXiv · 2306.07000

Bounding geometrically integral del Pezzo surfaces

Fabio Bernasconi·Gebhard Martin
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Abstract

We prove several boundedness statements for geometrically integral normal del Pezzo surfaces $X$ over arbitrary fields. We give an explicit sharp bound on the irregularity if $X$ is canonical or regular. In particular, we show that wild canonical del Pezzo surfaces exist only in characteristic 2. As an application, we deduce that canonical del Pezzo surfaces form a bounded family over $\mathbb{Z}$, generalising work of Tanaka. More generally, we prove the BAB conjecture on the boundedness of $\varepsilon$-klt del Pezzo surfaces over arbitrary fields of characteristic different from 2, 3, and 5.

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Fabio Bernasconi, Gebhard Martin. 2023-06-12. Bounding geometrically integral del Pezzo surfaces. https://doi.org/10.1017/fms.2024.80

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