The Vlasov equation for the collisionless evolution of the single-particle
probability distribution function (PDF) is a well-known example of coadjoint
motion. Remarkably, the property of coadjoint motion survives the process of
taking moments. That is, the evolution of the moments of the Vlasov PDF is also
coadjoint motion. We find that {\it geodesic} coadjoint motion of the Vlasov
moments with respect to powers of the single-particle momentum admits singular
(weak) solutions concentrated on embedded subspaces of physical space. The
motion and interactions of these embedded subspaces are governed by canonical
Hamiltonian equations for their geodesic evolution.