Abstract
In this paper we give a characterization of the height of K3 surfaces in characteristic
p>0
. This enables us to calculate the cycle classes in families of K3 surfaces of the loci where the height is at least
h
. The formulas for such loci can be seen as generalizations of the famous formula of Deuring for the number of supersingular elliptic curves in characteristic
p
. In order to describe the tangent spaces to these loci we study the first cohomology of higher closed forms.