A central leaf passing through a point in the Siegel modular variety (modulo ) of genus is the locus which consists of the points whose associated polarised -divisible groups are isomorphic to that of . We are interested in how the size of changes when varies in the moduli space. In particular how large can be (if finite) and when is a singleton (the Gauss problem). In this talk we shall discuss these questions and explain our result to the Gauss problem. This is joint work with Tomoyoshi Ibukiyama and Valentijn Karemaker.