In positive characteristic, K3 surfaces have an invariant called the height. Those with infinite height are called supersingular K3 surfaces, and for such surfaces one can further define an invariant called the Artin invariant.
Yobuko showed that the height of a K3 surface admits a reinterpretation in terms of Frobenius singularities, namely via the quasi-F-split height.
In this talk, I will discuss the relationship between the Artin invariant and quasi-F-splitting for smooth quartic K3 surfaces, and give an explicit formula for computing the Artin invariant.
This talk is based on joint work with Shou Yoshikawa.