Cycle classes on the moduli of K3 surfaces in positive characteristic

TL;DR

This paper derives explicit formulas for cycle classes of height and Artin invariant strata in families of K3 surfaces over positive characteristic fields, using a uniform approach with flag spaces and Pieri formulas.

Contribution

It introduces a uniform method to compute cycle classes of strata in K3 surface families, extending techniques from abelian varieties to K3 surfaces.

Findings

Explicit formulas for cycle classes of strata

Unified approach applicable to all strata

Uses flag space and Pieri formula techniques

Abstract

This paper provides explicit closed formulas in terms of tautological classes for the cycle classes of the height and Artin invariant strata in families of K3 surfaces. The proof is uniform for all strata and uses a flag space as the computations in [arXiv:math/0412272] for the Ekedahl-Oort strata for families of abelian varieties, but employs a Pieri formula formula to determine the push down to the base space.