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

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 $\mathbb{F}_7$.