Fedder type criteria for quasi-$F$-splitting

Abstract

Yobuko recently introduced the notion of quasi-F -splitting and F -split heights, which generalize and quantify the notion of Frobenius-splitting, and proved that F -split heights coincide with Artin-Mazur heights for Calabi-Yau varieties. In this paper, we prove Fedder type criteria of quasi-F -splittings of complete intersections, and in particular obtain an easy formula to compute Artin-Mazur heights of Calabi-Yau hypersurfaces. Moreover, as applications, we give explicit examples of quartic K3 surfaces over F 3 realizing all the possible Artin-Mazur heights, we provide explicit computations of F -split heights for all the rational double points and bielliptic surfaces, and introduce interesting phenomena concerned with inversion of adjunction, fiber products, Fano varieties, and general fibers of fibrations.