Foliations in Moduli Spaces of Abelian Varieties and Dimension of Leaves

In moduli spaces of abelian varieties and of p-divisible groups in characteristic p we have various foliations and statifications. In this paper we compute the dimensions of central leaves.We give three different proofs of these results, where every proof presents a different flavour of this beautiful topic. Components of Newton polygon strata for one fixed Newton polygon may have various different dimensions, according to properties of the polarizations considered; we show which dimensions do appear for a given Newton polygon. Hence dimensions of isogeny leaves can be computed this way.