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 ${\mathbb{F}}_7$.

18 Pages, 7 figures