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.
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Gerard van der Geer, Toshiyuki Katsura, On a stratification of the moduli of K3 surfaces. J. Eur. Math. Soc. 2 (2000), no. 3, pp. 259–290DOI 10.1007/S100970000021