On the reduction of the Siegel moduli space of abelian varieties of dimension 3 with Iwahori level structure

We study the moduli space of abelian threefolds with Iwahori level structure in positive characteristic. We explicitly determine the fibers of the canonical projection to the moduli space of principally polarized abelian varieties and draw conclusions about the relationship between the Ekedahl-Oort, the Kottwitz-Rapoport and the Newton stratification on these spaces