  We investigate Siegel modular varieties in positive characteristic with
Iwahori level structure. On these spaces, we have the Newton stratification,
and the Kottwitz-Rapoport stratification; one would like to understand how
these stratifications are related to each other. We give a simple description
of all KR strata which are entirely contained in the supersingular locus as
disjoint unions of Deligne-Lusztig varieties. We also give an explicit
numerical description of the KR stratification in terms of abelian varieties.
