K3 surfaces of any Artin-Mazur height over $\mathbb{F}_5$ and $\mathbb{F}_7$ via quasi-$F$-split singularities and GPU acceleration

Ryan Batubara; Jack J Garzella; Alex Pan

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arXiv · 2502.12428

K3 surfaces of any Artin-Mazur height over $\mathbb{F}_5$ and $\mathbb{F}_7$ via quasi-$F$-split singularities and GPU acceleration

Ryan Batubara·Jack J Garzella·Alex Pan

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Abstract

We develop a fast algorithm to calculate the Artin-Mazur height (equivalently, the quasi-$F$-split height) of a Calabi-Yau hypersurface, building on the work in arXiv:2204.10076. We provide a implementation of our approach, and use it to show that there are quartic K3 surfaces of any Artin-Mazur height over $\mathbb{F}_{5}$ and $\mathbb{F}_7$.

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Ryan Batubara, Jack J Garzella, Alex Pan. 2025-02-18. K3 surfaces of any Artin-Mazur height over $\mathbb{F}_5$ and $\mathbb{F}_7$ via quasi-$F$-split singularities and GPU acceleration. https://arxiv.org/abs/2502.12428

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