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K3 surfaces of any Artin-Mazur height over $\mathbb{F}_5$ and $\mathbb{F}_7$ via quasi-$F$-split singularities and GPU acceleration
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math.AGmath.ACmath.NT
keywords
heightmathbbartin-mazurquasi-splitsurfacesaccelerationalgorithm
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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