On a Stratification of the Moduli of K3 Surfaces

Details On a Stratification of the Moduli of K3 Surfaces On a Stratification of the Moduli of K3 Surfaces

1999-10-12

arxiv.org/abs/math/9910061v2

Mathematics

Algebraic Geometry

Plain Tex, 28 pages, minor changes in section 8

Scientific paper

In this paper we give a characterization of the height of K3 surfaces in positive characteristic. This enables us to calculate the cycle classes of the loci in families of K3 surfaces 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 positive characteristic. In order to describe the tangent spaces to these loci we study the first cohomology of higher closed forms.

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