  Consider all moduli points corresponding with polarized abelian varieties in
characteristic p such that the associated quasi-polarized p-divisible group is
geometrically isomorphic with a given one. This defines a subset C of the
moduli space. We show that C is closed in the corresponding open Newton polygon
stratum. In this way the stratum is the disjoint union of such "central
leaves". Under local-local isogenies we consider the orbit of one point: we
obtain a second type of leaves. Every stratum, up to a finite map, is the
product of one of its central leaves and one of its isogeny leaves. We expect
that these central leaves describe Hecke actions prime to p.
