  We study moduli spaces of abelian varieties in positive characteristic, more
specifically the moduli space of principally polarized abelian varieties on the
one hand, and the analogous space with Iwahori type level structure, on the
other hand. We investigate the Ekedahl-Oort stratification on the former, the
Kottwitz-Rapoport stratification on the latter, and their relationship. In this
way, we obtain structural results about the supersingular locus in the case of
Iwahori level structure, for instance a formula for its dimension in case $g$
is even.
