A stratification on the moduli of K3 surfaces in positive characteristic

TL;DR

This paper reviews the cycle classes of stratifications on the moduli space of K3 surfaces in positive characteristic, focusing on height and Artin invariant, and introduces a new irreducibility result for these strata.

Contribution

It provides a comprehensive review of existing results and establishes a new irreducibility theorem for the stratified moduli of K3 surfaces in positive characteristic.

Findings

Cycle classes of strata are characterized.

Strata defined by height and Artin invariant are studied.

New irreducibility result for these strata is proven.

Abstract

We review the results on the cycle classes of the strata defined by the height and the Artin invariant on the moduli of K3 surfaces in positive characteristic obtained in joint work with Katsura and Ekedahl. In addition we prove a new irreducibility result for these strata.