On a Stratification of the Moduli of K3 Surfaces

1999/10/12 by G. van der Geer, van der Geer, G., T. Katsura +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9910061

Plain Tex, 28 pages, minor changes in section 8

arxiv created 2000/01/06 · arxiv updated 2009/11/30

Abstract

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.

Related

• A stratification on the moduli of K3 surfaces in positive characteristic
• Cycle classes on the moduli of K3 surfaces in positive characteristic
• Existence of supersingular reduction for families of K3 surfaces with large Picard number in positive characteristic
• Maximal Brill-Noether loci via K3 surfaces
• Degeneration and curves on K3 surfac