On a stratification of the moduli of K3 surfaces

van der Geer, Gerard, and Katsura, T.. "On a stratification of the moduli of K3 surfaces." Journal of the European Mathematical Society 002.3 (2000): 259-290. <http://eudml.org/doc/277761>.

@article{vanderGeer2000,
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.},
author = {van der Geer, Gerard, Katsura, T.},
journal = {Journal of the European Mathematical Society},
keywords = {K3 surfaces; cycle classes; Deuring formula; supersingular elliptic curves; characteristic ; moduli of K3 surfaces; height of K3 surfaces; cycle classes},
language = {eng},
number = {3},
pages = {259-290},
publisher = {European Mathematical Society Publishing House},
title = {On a stratification of the moduli of K3 surfaces},
url = {http://eudml.org/doc/277761},
volume = {002},
year = {2000},
}

TY - JOUR
AU - van der Geer, Gerard
AU - Katsura, T.
TI - On a stratification of the moduli of K3 surfaces
JO - Journal of the European Mathematical Society
PY - 2000
PB - European Mathematical Society Publishing House
VL - 002
IS - 3
SP - 259
EP - 290
AB - 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.
LA - eng
KW - K3 surfaces; cycle classes; Deuring formula; supersingular elliptic curves; characteristic ; moduli of K3 surfaces; height of K3 surfaces; cycle classes
UR - http://eudml.org/doc/277761
ER -